Intermediate November 2020 Unit 2 Q11
11. The diagram shows two right-angled triangles, joined together along a common side.
AB = 10·8 cm, BC = 14·4 cm and CD = 24 cm.
Diagram not drawn to scale
Calculate the area of triangle ACD.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (AC2 =) 10·82 + 14·42 | M1 | Accept equivalent of using cos rule (as cos 90 = 0). |
| AC2 = 324 or (AC =) √324 | A1 | |
| (AC =) 18(cm) | A1 | F.T. √’their 324’ provided M1 gained. Final answer of AC = 324 is M1A0A0. |
| (Area ACD =) \(\dfrac{24 \times 18}{2}\) | M1 | FT ‘their stated AC’. (May be shown on the diagram) Accept equivalent of using ½ × 24 × 18 × sin 90 (as sin 90 = 1). |
| = 216 (cm2) | A1 |
Alternative method to find AC
| Scheme | Marks | Comments |
|---|---|---|
| A correct and complete method (using two trigonometric relationships) | M2 | |
| AC = 18(cm) | A1 |
In the original the alternative method is printed in the Comments column.