Foundation November 2020 Unit 2 Q17
17. In the diagram below, ABCD is a rectangle with AB = 5 cm.
ABP is a quarter of a circle with centre A.
AP = PD.
Diagram not drawn to scale
Calculate the area of the shaded section shown above.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (Length of AD or BC =) 10 (cm) | B1 | May be seen on the diagram or implied in later work. |
| (Area of ABCD = 5 × 10 =) 50 (cm2) | B1 | FT 5 × ‘their AD (or BC)’. The 50(cm2) may be shown as two areas of 25(cm2) for B1 B1. |
| (Area APB =) \(\dfrac{\pi \times 5^{2}}{4}\) | M1 | |
| = 19·6(…..)(cm2) | A1 | SC1 for sight of π × 52 or equivalent (78·5….) |
| (Shaded area = 50 − 19·6 =) 30·3(…) or 30·4(cm2) | B1 | FT ‘their stated area ABCD’ – ‘their stated area APB’ Note: Sight of (25 – ‘area of APB’) + 25 implies the first two B marks. [rectangle divided in half] |