Question

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

Answer 1

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

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
`(4)/(2)\cdot√(3)=2√(3)`. The area of this figure can be given as
`b\cdot h`, therefore our answer is
`5\cdot 2√(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
`(1)/(2)ab\sin C`. Since there are 2 of these triangles, the area of the entire figure is
`2\cdot(1)/(2)\cdot4\cdot 5\cdot \sin 60^(\circ)\approx \fbox{$17.3$}`.