Geometry and measures worksheet — GCSE Foundation

1.The top of a clock tower is 25 m above level ground. Oliver stands on the ground 25 m from the foot of the tower. Work out the angle of elevation of the top of the tower from the point where Oliver stands.

2.A sector of a circle has an angle of 90° and an arc length of 15.7 cm. Using π = 3.14, work out the radius of the circle.

3.Write down the exact value of tan 45°.

4.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

5.Postcard P is similar to postcard Q. The 6 cm side of P corresponds to the 15 cm side of Q, and the 8 cm side of P corresponds to a matching side of Q. Work out the length of that matching side of Q.

6.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

7.A solid has 10 vertices and 15 edges. Using the formula F + V − E = 2, work out how many faces it has.

8.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

9.A circular garden pond has a diameter of 5 m. A gardener is laying gravel around it in a ring-shaped path 1 m wide, measured outward from the edge of the pond. Work out the area of the gravel path. Use π = 3.14.

10.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

11.A solid has a plan view that is a circle, and a front elevation that is a triangle. Which solid is this?

12.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².

13.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

14.Two similar triangles have lengths in the ratio 2 : 5. The sides of the smaller triangle are 4 cm, 6 cm and 8 cm. Work out the length of the longest side of the larger triangle.

15.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.