Geometry and measures worksheet — GCSE Foundation

1.Two similar triangular tiles have lengths in the ratio 3 : 5. The longest side of the smaller tile is 9 cm. Work out the length of the longest side of the larger tile.

2.A circle has a radius of 3 cm. Work out the diameter of the circle.

3.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

4.Every diameter of a circle is an example of a more general type of straight line joining two points on the circle. Which term names that more general type of line?

5.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

6.A straight line touches the edge of a circle at exactly one point and does not cross into the circle at all. Write down the term for this line.

7.Work out the exact value of sin 45° × cos 45°.

8.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.

9.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

10.Triangle ABC is similar to triangle PQR. AB corresponds to PQ, and BC corresponds to QR. AB = 5 cm, PQ = 15 cm and BC = 7 cm. Work out the length of QR.

11.A rectangular photograph has an area of 96 cm². One of its sides is 8 cm long. Work out the length of the other side.

12.Write down the exact value of sin 60°.

13.Loose sweets are sold at £1.20 per 100 g. Work out the cost of 350 g of sweets.

14.The perimeter of a square is 20 cm. Work out the area of the square.

15.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?