Question
Find the area of the regular pentagon below by using the area formula for triangles. a = 4 inches and b = 6 inches
Answers
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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}}.
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}}.