2D & 3D Shapes (Edexcel GCSE Maths: Foundation): Exam Questions

is a straight line.
The lines , , and  are all the same length.
Angle . 

Work out the size of the angle marked .

Below are 4 different 3D shapes, labelled 

(i) Which of these shapes has the greatest number of faces, and how many does it have?

[1]

(ii) Which of these shapes has the least number of edges, and how many does it have?

[1]

(iii) Explain why shape B is not a prism. 

[1]

The diagram shows a prism with a cross section in the shape of a trapezium.

On the centimetre grid below, draw the front elevation and the side elevation of the prism.

Use a scale of 2 cm to 1 m.

Here are the names of 5 quadrilaterals.

Write the name of the correct shape for each of the descriptions below.

(i) All four sides are equal in length.
All four of the angles are identical.

[1]

(ii) There are two pairs of parallel sides.
The angles opposite each other are identical. 
There are no lines of symmetry.

[1]

(iii) All four of the sides have the same length.
None of the angles are 90°.

[1]

The grid shows a point and four quadrilaterals, and .

Write down the mathematical name of shape .

The diagram shows a cuboid.

On the 1 cm² grid, complete the net of the cuboid.
One face has been drawn for you.

The diagram shows the net of a triangular prism on a 1cm² grid.

Write down the mathematical name for the type of triangle shown on the grid.

Complete each statement.

A quadrilateral with only one pair of parallel sides is called a ...............................................

An angle greater than 90° but less than 180° is called ...............................................

On the 1cm² grid, complete the net of this box.

The diagram shows a net of a solid.

Write down the mathematical name of the solid.

The diagram shows a quadrilateral on a 1 cm² grid.

Write down the mathematical name of this quadrilateral.

is a straight line.
is a triangle.
is a parallelogram.

Show that triangle  is an isosceles triangle. Give a reason for each stage of your working.

The diagram shows the kite, .

The lengths  and  are equal.

Find the values of  and .

A square-based right pyramid has a base with sides of length 4 cm.

The sides of the pyramid are isosceles triangles.

The vertical height of the pyramid is 5 cm.

Sketch the plan, front, and side elevations of the pyramid. 

Label the dimensions on your diagram.

The perpendicular height of each triangular face is 5.4 cm.

Calculate the surface area of the pyramid.

A cuboid measures 6 cm by 3 cm by 1 cm.

i) On the 1 cm² grid, draw an accurate net of this cuboid.

One face has been drawn for you.

[3]

ii) Calculate the surface area of the cuboid.

.......................................... cm² [2]

A cuboid has length 5 cm, width 4 cm and height 3 cm.

On the 1 cm² grid, complete the net of the cuboid.
One face has been drawn for you.

Find the volume of the cuboid.

.......................................... cm³ 

The diagram shows the net of a solid on a 1cm² grid.

i) Write down the mathematical name for the solid.

[1]

ii) Work out the volume of the solid.

.......................................... cm³ [2]

A cuboid has length 3 cm, width 2 cm and height 1cm.

On the 1 cm² grid, draw a net of the cuboid.

A cuboid measures 6cm by 3cm by 2 cm.
On this 1cm² grid, draw a net of the cuboid.

The diagram shows a net of a cube.

i) The square labelled  is the base.

Write the letter  in the square that is the top of the cube.

[1]

ii) On the grid, draw a different net of this cube.

[1]