Find the area of the regular pentagon below by using the area formula for triangles. a = 4 inches and b = 6 inches
A.
60 in^2
B.
10 in^2
C.
120 in^2
D.
24 in^2
C. 120 in^2
explain
To find the area of a regular pentagon, you can divide it into congruent triangles and calculate the area of one of the triangles.
The formula for the area of a triangle is:
Area = (1/2) * base * height
In this case, we have a triangle with a base of 4 inches and a height of 6 inches.
Plugging in the values into the formula:
Area = (1/2) * 4 inches * 6 inches
Calculating:
Area = (1/2) * 24 square inches
Area = 12 square inches
Since each side of the pentagon has the same triangle, we can multiply the area of one triangle by 5 to find the total area of the pentagon.
Total area of the pentagon = 12 square inches * 5 triangles = 60 square inches
Therefore, the answer is A. 60 in^2.
To find the area of a regular pentagon using the area formula for triangles, we can break down the pentagon into five congruent triangles.
The area formula for a triangle is given by the formula A = (1/2) * base * height.
In this case, let's use a as the base and b as the height of each triangle.
Therefore, the area of one triangle is (1/2) * 4 inches * 6 inches = 12 square inches.
Since there are five congruent triangles in a regular pentagon, the total area of the pentagon is 5 * 12 square inches = 60 square inches.
Therefore, the correct answer is A. 60 in^2.