Geometry and measures worksheet — GCSE Foundation

1.A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.

2.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.

3.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

4.p is the column vector with top number 2 and bottom number 3. q is the column vector with top number −1 and bottom number 4. Work out 2p + q, giving your answer as a column vector in the form (top, bottom).

5.A jug holds 750 ml of water. Work out what fraction of a litre this is.

6.Write down the exact value of tan 0°.

7.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

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

9.Write down the name given to a triangle whose three sides are all the same length.

10.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.

11.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

12.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

13.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

14.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

15.A tile manufacturer cuts a hexagonal tile so that all six sides measure exactly 4 cm, but a check shows only two pairs of the six interior angles are equal to each other, not all six angles. The customer's order specifies regular hexagonal tiles. Based on the check, is this tile a regular hexagon?