A trapezium is constructed on a grid of 10 rectangles.
Each rectangle measures 3 cm × 7 cm.
What is the area of the trapezium?
- \(150\ \text{cm}^2\)
- \(168\ \text{cm}^2\)
- \(189\ \text{cm}^2\)
- \(210\ \text{cm}^2\)
Show Worked Solution
\(\text{Method 1: Composite}\)
| \(\therefore\ \text{Total Area}\) | \(=\text{Area 1 rectangle}+2\times\ \text{Area of triangle}\) |
| \(=6\times 21+2\times\Bigg(\dfrac{1}{2}\times 3\times 14\Bigg)\) | |
| \(=126+42\) | |
| \(=168\ \text{cm}^2\) |
\(\text{Method 2: Trapezium}\)
| \(\text{Area}\) | \(=\dfrac{h}{2}(a+b)\) |
| \(=\dfrac{14}{2}(15+9)\) | |
| \(=168\ \text{cm}^2\) |
\(\Rightarrow B\)