Question

Find the area of the regular polygon. Round to the nearest tenth. given is 12 in

Answer 1

Area = 62.4 in²

Explanation:

This is an equilateral triangle. Find its height (from pythogras theorem):

`{ \tt{height = \sqrt{12 {}^(2) - 6 {}^(2) } }} \\ { \tt{height = √(108) }} \\ { \tt{height = 10.392 \: in}}`

Find area of the two right angled triangles:

`{ \tt{area = 2( (1)/(2) * base * height)}} \\ \\ { \tt{area = 2( (1)/(2) * 6 * 10.392) }} \\ \\ { \tt{area = 6 * 10.392}} \\ \\ { \underline{\tt{ \: area = 62.4 \: in {}^(2) \: }}}`