Find the area of the regular pentagon below by using the area formula for triangles. a = 6 inches and b = 8 inches
To find the area of the regular pentagon, we can divide it into 5 congruent triangles and then find the area of one triangle and multiply it by 5.
First, let's find the height (h) of one of the triangles by using the Pythagorean theorem:
h = sqrt((8^2) - (6^2))
h = sqrt(64 - 36)
h = sqrt(28)
h ≈ 5.29 inches
Now, we can find the area of one triangle:
Area of triangle = (1/2) * base * height
Area of triangle = (1/2) * 6 * 5.29
Area of triangle ≈ 15.87 square inches
Therefore, the area of the whole regular pentagon is:
Area of pentagon = 5 * Area of one triangle
Area of pentagon = 5 * 15.87
Area of pentagon = 79.35 square inches
So, the area of the regular pentagon with side lengths of 6 inches and 8 inches is 79.35 square inches.