Find the area of the regular pentagon below by using the area formula for triangles. a = 4 inches and b = 6 inches
To use the area formula for triangles, we need to draw lines from one corner of the pentagon to the opposite corner, creating five congruent triangles.
Each triangle has a base of 6 inches and a height of 2√(4^2 - 3^2) = 2√7 inches (using the Pythagorean theorem).
Therefore, the area of one triangle is (1/2)bh = (1/2)(6 inches)(2√7 inches) = 6√7 square inches.
Since there are five congruent triangles in the pentagon, the total area is 5 times the area of one triangle:
Area = 5(6√7 square inches) = 30√7 square inches. Answer: \boxed{30\sqrt{7}}.
To find the area of the regular pentagon, we need to divide it into smaller triangles. Since it is a regular pentagon, each interior angle is 108 degrees, and each exterior angle is 72 degrees.
Step 1: Divide the pentagon into 5 congruent triangles by drawing diagonals from one vertex to all other non-adjacent vertices.
Step 2: Each triangle formed will have a base of length 6 inches and a height of 4 inches.
Step 3: Calculate the area of one triangle using the formula for the area of a triangle: Area = (base × height) / 2.
Area = (6 inches × 4 inches) / 2 = 12 square inches.
Step 4: Since the pentagon is composed of five congruent triangles, multiply the area of one triangle by 5 to find the total area of the pentagon.
Total area of the pentagon = 5 × 12 square inches = 60 square inches.
Therefore, the area of the regular pentagon is 60 square inches.