Foundation November 2016 Unit 1 Q17
17. A right-angled triangle BCD is joined to a rectangle ABDE, as shown below.
Diagram not drawn to scale
The area of the rectangle is 45 cm2.
Calculate the area of the right-angled triangle.
You must show your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (BD or AE) × 9 = 45 OR (BD or AE =) 45/9 | M1 | Accept any unambiguous reference to or notation for BD and AE. Allow use of ‘height’ or ‘width’. |
| (BD or AE =) 5(cm) | A1 | May be seen on the diagram. |
| (CD =) 6(cm) | B1 | May be seen on the diagram. |
| (Area of triangle =) \(\dfrac{5 \times 6}{2}\) | M1 | F.T. ‘their 5’ provided it clearly represents BD. F.T. ‘their 6’ provided it clearly represents CD. |
| = 15(cm2) | A1 | No marks for an unsupported 15 BUT 15cm2 gains all 5 marks. |
Alternative
Alternative method.
| Scheme | Marks | Comments |
|---|---|---|
| 9 × (BD or AE) = 45 OR (BD or AE =) 45/9 | M1 | |
| (BD or AE) = 5(cm) | A1 | |
| (Area of trapezium =) \(\dfrac{9 + 15}{2} \times 5\) | M1 | (F.T. ‘their 5’) |
| = 60(cm2) | A1 | |
| (Area of triangle = 60 – 45 =) 15(cm2) | A1 |