Question

find the area of a regular hexagon with an apothem 10.4 yards long and side 12 yards long. Round your answer to the nearest tenth

Answer 1

Answer:

The area of  a regular hexagon with an apothem 10.4 yards long and side 12 yards long is 124.80 yards²

Step-by-step explanation:

Given : A regular hexagon with an apothem 10.4 yards long and side 12 yards long.

We have to find the area of a regular hexagon with an apothem 10.4 yards long and side 12 yards long.  

Since, the Given hexagon is a regular hexagon.

So, each side make equal angle with mid point.

Thus, Area of each triangle = $\frac{1}{2} \times base \times height$

base = 12 yards

height = 10.4 yards.

Thus, Area of each triangle = $\frac{1}{2} \times 12 \times 10.4=62.4$

Since, there are 6 triangles.

so area of hexagon = 6 × Area of triangle

area of hexagon = 6 × 62.4 = 124.8 yards²

Thus, The area of  a regular hexagon with an apothem 10.4 yards long and side 12 yards long is 124.80 yards²

Answer 2

The area of a regular polygon is given by the formula below. area = (½)(apothem) (perimeter). We calculate as follows:

perimeter = 6(side length) = 6(12) = 72 yards

Area =  (½) (apothem) (perimeter)
Area =  (½)(10.4) (72)
Area = 374.4 yd^2