The floor of a chicken coop is in the shape of a trapezium.
The floor, \(ABCD\), and the chicken coop are shown below.
\(AB = 3\ \text{m}, BC = 2\ \text{m and}\ \ CD = 5\ \text{m.}\)
- What is the area of the floor of the chicken coop?
Write your answer in square metres. (2 marks)
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- What is the perimeter of the floor of the chicken coop?
Write your answer in metres, correct to one decimal place. (2 marks)
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Show Worked Solution
| a. | \(A\) | \(=\dfrac{h}{2}(a+b)\) |
| \(=\dfrac{2}{2}\times (3 + 5)\) | ||
| \(=8\ \text{m}^2\) |
| b. |  |
\(\text{Using Pythagoras,}\)
| \(AD^2\) | \(=2^2+2^2\) |
| \(AD^2\) | \(=8\) |
| \(AD\) | \(=\sqrt{8}\) |
| \(=2.82\dots\ \text{m}\) |
| \(\therefore\ \text{Perimeter}\) | \(=3+2+5+2.82\dots\) |
| \(=12.8\ \text{m (1 d.p.)}\) |