Geometry and measures, Year 8: more practice

(4, 5)

提示Reverse the movement: go back 4 right and 1 down.

为什么Before the move B was 4 to the right and 1 lower: (0 + 4, 6 − 1) = (4, 5). Check: 4 left and 1 up from (4, 5) lands on (0, 6).

14 m²

提示Multiply the base by the perpendicular height.

为什么3.5 × 4 = 14, in square metres.

32 cm²

提示Find the mean of the parallel sides, then multiply by the height.

为什么Mean of the parallel sides is (6 + 10) ÷ 2 = 8, and 8 × 4 = 32 cm².

5 cm

提示Write the area formula with h as the unknown, then solve.

为什么45 = ½ × (7 + 11) × h = 9h, so h = 5. Check: ½ × 18 × 5 = 45.

25.1 cm

提示Circumference is π times the diameter, and the diameter is twice the radius.

为什么d = 8 cm, so C = π × 8 = 25.13… ≈ 25.1 cm.

(1, −2)

提示Picture the point turning like a clock hand. It starts to the right of and above the origin and ends below.

为什么A 90° clockwise turn sends (x, y) to (y, −x). The point lands 1 right and 2 down, at (1, −2).

56 cm

提示Find the new side lengths first.

为什么The sides become 8 cm and 20 cm, so the perimeter is 2 × (8 + 20) = 56 cm. The original perimeter, 14 cm, is also multiplied by 4.

108 cm³

提示Volume of a prism = area of cross-section × length.

为什么12 × 9 = 108, and the units are cubic because three lengths are multiplied.

25

提示Work backwards: volume = cross-section area × length.

为什么150 ÷ 6 = 25. Check: 25 × 6 = 150.

52 cm²

提示A cuboid has three pairs of identical faces.

为什么The faces are 2 × 3 = 6, 2 × 4 = 8 and 3 × 4 = 12. The total is 2 × (6 + 8 + 12) = 52 cm².