E4.2 2D Shapes: Perimeters & Areas
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1 E4.2 2D Shapes: Perimeters & Areas Question Paper Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Level Extended Topic E4. Mensuration (Perimeters, Areas and Volumes) Sub-Topic E4.2 2D Shapes: Perimeters & Areas Booklet Question Paper Time Allowed: 57 minutes Score: / 47 Percentage: /100 Grade Boundaries: A* A B C D E U >85% 75% 60% 45% 35% 25% <25%
2 1. D 8 cm C 8 cm A 12 cm B Calculate the area of this trapezium.... cm 2 [4] 2. The base of a triangle is 9 cm correct to the nearest cm. The area of this triangle is 40 cm 2 correct to the nearest 5 cm 2. Calculate the upper bound for the perpendicular height of this triangle cm [3] 6 cm 5 cm x cm The area of this parallelogram is 51.5 cm 2. Work out the value of x. x =... [2]
3 4. The scale on a map is 1 : The area of a lake on the map is 1.6 square centimetres. Calculate the actual area of the lake. Give your answer in square metres....m 2 [3] 5 E A (x 4) cm B (x 1) cm 7 cm D C F G (a) ABCD is a square. Find the value of x. Answer(a) x =... [1] (b) Square ABCD and isosceles triangle EFG have the same perimeter. Work out the length of FG. Answer(b) FG =... cm [2]
4 6 8 m 5 m 5 m 12 m The diagram shows the front face of a barn. The width of the barn is 12 m. The height of the barn is 8 m. The sides of the barn are both of height 5 m. (a) Work out the area of the front face of the barn. Answer(a)... m 2 [3] (b) The length of the barn is 15 m. Work out the volume of the barn. 15 m Answer(b)... m 3 [1]
5 7 An equilateral triangle has sides of length 6.2 cm, correct to the nearest millimetre. Complete the statement about the perimeter, P cm, of the triangle. Answer... P... [2] 8 The circumference of a circle is 30 cm. (a) Calculate the radius of the circle. Answer(a)... cm [2]
6 (b) The length of the arc of the semi-circle is 15 cm. Calculate the area of the semi-circle. Answer(b)... cm 2 [2]
7 cm R P 10 cm Q The area of triangle PQR is 38.5 cm 2. Calculate the length QR. Answer QR =... cm [6]
8 10 (a) A sector of a circle has radius 12 cm and an angle of 135. (i) Calculate the length of the arc of this sector. Give your answer as a multiple of π cm Answer(a)(i)... cm [2] (ii) The sector is used to make a cone. (a) Calculate the base radius, r. h 12 cm r Answer(a)(ii)(a) r =... cm [2] (b) Calculate the height of the cone, h. Answer(a)(ii)(b) h =... cm [3]
9 (b) The diagram shows a plant pot. It is made by removing a small cone from a larger cone and adding a circular base.
10 This is the cross section of the plant pot. 15 cm (i) Find l. 35 cm 8 cm l Answer(b)(i) l =... cm [3] (ii) Calculate the total surface area of the outside of the plant pot. [The curved surface area, A, of a cone with radius r and slant height l is A = πrl.] Answer(b)(ii)... cm 2 [3]
11 (c) Some cones are mathematically similar. For these cones, the mass, M grams, is proportional to the cube of the base radius, r cm. One of the cones has mass 1458 grams and base radius 4.5 cm. (i) Find an expression for M in terms of r. Answer(c)(i) M =... [2] (ii) Two of the cones have radii in the ratio 2 : 3. Write down the ratio of their masses. Answer(c)(ii)... :... [1]
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