Foundation June 2019 Unit 1 Q15
15. In the diagram below, ABCE is a square and CDE is a right-angled triangle.
The length of DE is 4 cm and the area of triangle CDE is 14 cm2.
Calculate the area of the whole shape ABCDE.
You must show all your working. [4]
Diagram not drawn to scale
| Scheme | Marks | Comments |
|---|---|---|
| (Area of the triangle CDE =) \(14 = \dfrac{4 \times \text{CE}}{2}\) | M1 | Lengths may be shown on the diagram. Accept equivalent e.g. 28 = 4 × CE. |
| (CE =) 7 (cm) | A1 | |
| (Area ABCE = 7 × 7 =) 49 (cm2) | B1 | FT ‘their stated or shown length CE’. |
| (Area of whole shape = 49 + 14 =) 63 (cm2) | B1 | FT ‘their stated or shown area of square’ + 14. |
Alternative
15. Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Area of the triangle CDE =) \(14 = \dfrac{4 \times \mathit{CE}}{2}\) | M1 | Lengths may be shown on the diagram. |
| (CE =) 7 (cm) | A1 | |
| (Area Trapezium ABCD = ) \(\dfrac{[(7 + 4) + 7] \times 7}{2}\) = 63 (cm2) | M1 A1 | FT ‘their stated or shown length CE (=CB)’ consistently as ‘their 7’. |
The scheme prints this alternative in italics.