Higher November 2022 Unit 2 Q13
13. Two similar shapes have perimeters of 241 cm and 719 cm.
The area of the smaller shape is 2063 cm2.
Calculate the area of the larger shape.
Give your answer in m2. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Area scale factor =) (719/241)2 OR (241/719)2 | B1 | Or equivalent. |
| 2063 × (719/241)2 OR 2063 ÷ (241/719)2 | M1 | FT ‘their linear scale factor squared’. |
| =18362(·124…cm2) | A1 | CAO allowing only these values: 18000 OR 18300 up to 18800 OR 19000 |
| = 1·8(…m2) | B1 | Strict FT of a correct conversion of ‘their area’ to m2. Allow 1·9(…m2) from correct working. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Area of smaller shape = 2063÷10000 =) 0.2063 (m2) | B1 | |
| (Area scale factor =) (719/241)2 OR (241/719)2 | B1 | Or equivalent. |
| 0.2063 × (719/241)2 OR 0.2063 ÷ (241/719)2 | M1 | FT ‘their linear scale factor squared’ AND Strict FT of ‘their conversion of the smaller area’ to m2. |
| = 1·8(…m2) | A1 | Allow 1·9(…m2) from correct working. |