Question

Find the area of the regular polygon.
Round to the nearest tenth.
16 fi
[ ? ] ft2

Answer 1

Answer:

110.9ft²

Step-by-step explanation:

The given regular polygon is a triangle.

Therefore it is an equilateral triangle.

Area of an equilateral triangle is given by:

$A = \frac{ \sqrt{3} }{4} {s}^{2}$

Where s is the magnitude of one side.

From the given diagram, the side of the equilateral triangle is s=16ft.

$A = \frac{ \sqrt{3} }{4} \times {16}^{2}$

This implies that:

$A = \frac{ \sqrt{3} }{1} \times 4 \times 16 {ft}^{2}$

This simplifies to:

$A = 64 \sqrt{3} {ft}^{2}$

$A = 110.85$

The area to the nearest tenth is 110.9 ft²