Question

Find the area of the figure. Round your answer to the nearest tenth.​

Answer 1

Answer:

$17.3\:\mathrm{m^2}$

Step-by-step explanation:

Solution 1:

As the angles are marked, the figure forms a 30-60-90 right triangle with the height. Therefore the height will be  $\frac{4}{2}\cdot\sqrt{3}=2\sqrt{3}$. The area of this figure can be given as $b\cdot h$, therefore our answer is $5\cdot 2\sqrt{3}\approx \fbox{ 17.3 }$.

Solution 2:

The figure forms two triangles when cut by the shortest diagonal. The area of a triangle can be given by $\frac{1}{2}ab\sin C$. Since there are 2 of these triangles, the area of the entire figure is $2\cdot\frac{1}{2}\cdot4\cdot 5\cdot \sin 60^{\circ}\approx \fbox{ 17.3 }$.