Area and perimeter

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A rectangle and a semicircle are joined to make the shape below.

The height of the rectangle is 10 cm. The area of the rectangle is 400 cm².

Calculate the radius of the semicircle.

You must show all your working.

The diagram below shows a trapezium, ABCD.

The area of the right-angled triangle, AED, is 24 cm². The length of AB is 3 cm. The length of DE is 4 cm. The length of EC is 10 cm. Calculate the area of the trapezium, ABCD.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A square and an equilateral triangle are shown below.

The length of a side of the square is 12 cm. The perimeter of the square is equal to the perimeter of the equilateral triangle.

Calculate the length of a side of the equilateral triangle.

You must show all your working.

The diagram below shows a sketch of a circle that fits exactly inside a square.

The radius of the circle is 5 cm.

Calculate the total area of the shaded regions. Give your answer as a decimal.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing. The diagram below shows a trapezium, ABCD.

The area of the right-angled triangle, AED, is 24 cm². The length of AB is 3 cm. The length of DE is 4 cm. The length of EC is 10 cm. Calculate the area of the trapezium, ABCD.

You must show all your working.

The diagram below shows a sketch of a circle that fits exactly inside a square.

The radius of the circle is 5 cm.

Calculate the total area of the shaded regions. Give your answer as a decimal.

You must show all your working.

Owen says,

Is Owen correct?

Show clearly, using an example, how you decided.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Owen says,

Is Owen correct?

Show clearly, using an example, how you decided.

The diagram shows a solid cylinder with radius 10 cm.

The total surface area of the solid cylinder is 1570·8 cm².

Find the height of the cylinder.

The diagram shows a solid cylinder with radius 10 cm.

The total surface area of the solid cylinder is 1570·8 cm².

Find the height of the cylinder.

Calculate the area of a circle with a radius of 8·7 cm.

Give your answer in cm², correct to the nearest whole number.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The right-angled triangle A B C is a cross-section of a prism, as shown below. A B = 9 cm, B C = 10 cm and A B C = 90°. The length of the prism is 20 cm.

Calculate the volume of the prism. You must show all your working. [4 + 2 OCW]

The diagram below shows a shape made by joining two rectangles together.

The area of the whole shape is 89 cm².

Form and solve an equation to find the value of x.

A kite and an isosceles triangle are shown below.

They are not drawn to the same scale.

Using the information shown on the kite, calculate the perimeter of the isosceles triangle. Do not use a trial and improvement method.

You must show all your working.

Calculate the circumference of a circle with a radius of 38 cm.

Give your answer in cm, correct to 2 significant figures.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The right-angled triangle A B C is a cross-section of a prism, as shown below. A B = 9 cm, B C = 10 cm and A B C = 90°. The length of the prism is 20 cm.

Calculate the volume of the prism.

You must show all your working.

The diagram below shows a shape made by joining two rectangles together.

The area of the whole shape is 89 cm².

Form and solve an equation to find the value of x.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram below shows a shape made by joining two identical rectangles together. Each rectangle is 8 cm long and 5 cm wide. The length of AB is 6 cm.

Calculate the perimeter of the shape.

You must show all your working.

The diagram below shows two shaded squares inside a larger square.

The diagram shows the area of each of the two shaded squares.

Calculate the total area of the two regions that have not been shaded.

You must show all your working.

The diagram shows two circles that fit in a rectangle.

The centre of the small circle is directly below the centre of the large circle. The diameter of the small circle is 8 cm. The radius of the large circle is 2 cm greater than the radius of the small circle.

Calculate the total area of the shaded parts of the rectangle.

The diagram shows two circles that fit in a rectangle.

The centre of the small circle is directly below the centre of the large circle. The diameter of the small circle is 8 cm. The radius of the large circle is 2 cm greater than the radius of the small circle.

Calculate the total area of the shaded parts of the rectangle.

Find the volume of the solid prism shown above.

The solid prism is made of gold. Gold has a density of 19∙3 g/cm³. Calculate the mass of the prism.

Give your answer in kilograms.

Find the volume of the solid prism shown above.

The solid prism is made of gold. Gold has a density of 19∙3 g/cm³. Calculate the mass of the prism.

Give your answer in kilograms.

ABCD is a rectangle.

A is the point (3, 4), B is the point (–5, 4), C is the point (–5, –2) and D is the point (3, –2).

What is the perimeter of ABCD?

You may use the centimetre-squared grid below to help you.

The area of a rectangle is 80 cm².

Diagram not drawn to scale

The length of the rectangle is 5 times its width.

Calculate the length and width of the rectangle.

The diagram below shows a semicircle, with radius r, drawn inside a trapezium.

The area of the semicircle is 77 cm².

The semicircle touches the line AB. AB = 22 cm.

Calculate the area of the trapezium ABCD.

Show that 16x² 8x 3 0.

Solve the equation 16x² 8x 3 0.

You must use an algebraic method.

Find the length of BC.

You must justify any decision that you make.

The diagram below shows a semicircle, with radius r, drawn inside a trapezium.

The area of the semicircle is 77 cm².

The semicircle touches the line AB. AB = 22 cm.

Calculate the area of the trapezium ABCD.

A rectangle and a square are shown below.

The total area of the two shapes is 184 cm².

Find the perimeter of the square.

A rectangle and a square are shown below.

The total area of the two shapes is 184 cm².

Find the perimeter of the square.

A, B and C are points on the circumference of a circle with centre O.

The length of BC is 10 cm. The diameter of the circle is 18 cm.

Calculate the shaded area.

You must show all your working.

The rectangle below has: • a length of 3y • a width of y + a • an area of 3y² +12y.

Find the value of a.

You must show all your working.

Another rectangle has a width of 4x 10.

Given that x is a whole number, explain why the value of x cannot be less than 3.

The perimeter of the rectangle is 14x 4.

Find the length of the rectangle in terms of x.

A rectangle has a width of 4x 10.

The perimeter of the rectangle is 14x 4.

Find the length of the rectangle in terms of x.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A, B and C are points on the circumference of a circle with centre O. The length of BC is 10 cm. The diameter of the circle is 18 cm.

Calculate the shaded area.

You must show all your working.

A rectangle and a trapezium are shown below.

The area of the rectangle = 48 m². The width of the rectangle is represented by x. The height of the trapezium is twice the width of the rectangle.

Calculate the area of the trapezium.

You must show all your working.

The length of a rectangle is double its width. The area of the rectangle is greater than 60 cm². The perimeter of the rectangle is less than 40 cm.

Give a possible width and length of the rectangle. Calculate the area and the perimeter of this rectangle. You must show all your working.

Use the answer spaces to clearly identify which is the area and which is the perimeter.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A rectangle and a trapezium are shown below.

The area of the rectangle = 48 m². The width of the rectangle is represented by x. The height of the trapezium is twice the width of the rectangle.

Calculate the area of the trapezium.

You must show all your working.

The length of a rectangle is double its width. The area of the rectangle is greater than 60 cm². The perimeter of the rectangle is less than 40 cm.

Give a possible width and length of the rectangle. Calculate the area and the perimeter of this rectangle. You must show all your working.

Use the answer spaces to clearly identify which is the area and which is the perimeter.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A rectangle has length 15 cm and width 7 cm. A square has the same perimeter as this rectangle.

Calculate the length of a side of the square.

You must show all your working.

In the diagram below, ABCD is a rectangle with AB = 5 cm.

ABP is a quarter of a circle with centre A. AP = PD.

Calculate the area of the shaded section shown above.

You must show all your working.

In the diagrams below, ABCD is a square.

Triangles ABE and KLM are congruent.

Calculate the area of the square ABCD.

A circle, centre O, has a radius of 4 cm. A and B are points on the circumference of the circle. Lines PA and PB are both tangents to the circle. PB = 12 cm.

What is the length of PA?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

What is the size of PAO ?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

Calculate the area of the quadrilateral PAOB.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

In the diagram below, ABCD is a rectangle with AB = 5 cm. ABP is a quarter of a circle with centre A. AP = PD.

Calculate the area of the shaded section shown above.

You must show all your working.

The diagram shows two right-angled triangles, joined together along a common side.

AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.

Calculate the area of triangle ACD.

You must show all your working.

A circle, centre O, has a radius of 4 cm. A and B are points on the circumference of the circle. Lines PA and PB are both tangents to the circle. PB = 12 cm.

What is the length of PA?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

What is the size of PAO ?

State the circle theorem you have used to find your answer.

Circle theorem:_{……........ ……..}

Calculate the area of the quadrilateral PAOB.

A circle has radius r cm, where r is an integer.

The side of a square is of length xcm.

If the circle and square have the same area, explain why x cannot be an integer.

You should consider algebraic expressions in your answer.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram shows two right-angled triangles, joined together along a common side. AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.

Calculate the area of triangle ACD.

You must show all your working.

The diagram below shows a rectangle ABCF and a trapezium CDEF.

AF = 7 cm, ED = 8 cm and the perpendicular distance between FC and ED is 6 cm. The area of the rectangle ABCF is 91 cm².

7 cm

A B

Diagram not drawn to scale

Calculate the area of the trapezium CDEF.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram below shows a rectangle ABCF and a trapezium CDEF. AF = 7 cm, ED = 8 cm and the perpendicular distance between FC and ED is 6 cm. The area of the rectangle ABCF is 91 cm².

7 cm

A B

Diagram not drawn to scale

Calculate the area of the trapezium CDEF.

You must show all your working.

The right-angled triangle ABC has an area of 84 cm².

AB = 24 cm.

Calculate the perimeter of the triangle ABC.

You must show all your working.

Show that 2x² + 3x – 50 = 0.

Solve the equation 2x² + 3x – 50 = 0 to calculate the lengths AB and DC.

Give your answers correct to 1 decimal place.

Length of AB =_{……........ ……..} cm Length of DC =_{……........ ……..} cm

A rhombus has an area of 36∙8 cm². The rhombus is enlarged by a scale factor of 7.

Calculate the area of the enlarged rhombus.

Draw a reflection of this shape in the line PQ.

Catrin makes the following statement.

Is Catrin correct?

Show clearly, using an example, how you came to your decision.

Catrin makes the following statement.

Is Catrin correct?

Show clearly, using an example, how you came to your decision.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

Mair draws three different rectangles. Each rectangle has an area of 20 cm². Each of the sides of her rectangles is a whole number of centimetres.

Find the perimeter of each of Mair’s rectangles.

You must show all your working.

ABCE is a square.

Calculate the area of the shape ABCDE shown below.

ABCE is a square.

Calculate the area of the shape ABCDE shown below.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The perimeter of a square is 76.4 m.

Calculate the length of its diagonal.

You must show all your working.

Rectangle A is drawn on the centimetre square grid below.

What is the perimeter of rectangle A?

What is the area of rectangle A?

Give the units of your answer.

In the diagram below, ABCE is a square whose perimeter is 28 cm. CDE is a right-angled triangle whose area is 35 cm².

Calculate the length of DE.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

In the diagram below, ABCE is a square whose perimeter is 28 cm. CDE is a right-angled triangle whose area is 35 cm².

Calculate the length of DE.

You must show all your working.

Calculate the area of the trapezium shown below.

You must give the units of your answer.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

AB is the diameter of a circle, centre O, with radius OA = 4·2 cm. ABCD is a square.

Calculate the area of the shaded region.

You must show all your working.

A triangular prism of length 2 metres is shown below.

AC = 21 cm, BC = 35 cm and BAC = 90°.

Calculate the area of triangle ABC. Give your answer in cm².

You must show all your working.

Calculate the volume of the prism.

You must give the units of your answer.

A triangular prism of length 2 metres is shown below.

AC = 21 cm, BC = 35 cm and BAC = 90°.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing. Calculate the area of triangle ABC. Give your answer in cm².

You must show all your working.

Calculate the volume of the prism.

You must give the units of your answer.

A cone is joined to a cylinder, as shown below.

The cone has a base radius of 11 cm and a slant height of 13 cm. The cylinder has the same radius, 11 cm, and a height of 17 cm.

Calculate the total surface area of the composite solid.

The shape above has been drawn on a centimetre square grid.

Estimate the area of the shape.

In the diagram below,

• ABCD is a rectangle, and • PQ is parallel to AD.

D g cm Q 8 cm C

The area of is 52 cm². The area of is 20 cm². Calculate the values of f and g.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

ABCF is a rectangle. CDEF is a trapezium. BD is a straight line.

AB = 7 cm, BD = 9 cm and DE = 3 cm. The perimeter of rectangle ABCF is 24 cm. Calculate the area of the trapezium CDEF.

You must show all your working.

The area of triangle ABD, shown in the diagram below, is 35 cm².

AD = 5 cm and BC = 32 cm. D is on the line AC, and BD is perpendicular to AC.

Calculate the size of angle x.

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The area of triangle ABD, shown in the diagram below, is 35 cm². AD = 5 cm and BC = 32 cm. D is on the line AC, and BD is perpendicular to AC.

Calculate the size of angle x.

You must show all your working.