A pentagonal prism has a base area of 124 square inches. The lateral area (area of the sides) is made up of 5 equal-sized rectangles that are each 80 square inches. What is the surface area of the pentagonal prism?

Question

Mathematics

Joselyn

28 August, 21:14

A pentagonal prism has a base area of 124 square inches. The lateral area (area of the sides) is made up of 5 equal-sized rectangles that are each 80 square inches. What is the surface area of the pentagonal prism?

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Kolby Leon · Answer 1

Prism

Total surface area of the pentagonal prism is 648 square inches

Step-by-step explanation:

In geometry, a pentagon is defined as a five-sided polygon. In a simple pentagon the sum of the internal angles is 540°.

The pentagon base area = 124 square inches

In a pentagonal prism there are two such surfaces (top & bottom)

Hence the area of two pentagons = 124 * 2 = 248 square inches

The lateral area (area of the sides) is made up of 5 equal-sized rectangles

Area of one such rectangle is 80 square inches

Area of five such rectangle is 80 * 5 = 400 square inches

Total surface area of the pentagonal prism = 248 + 400 = 648 square inches

Hence, Total surface area of the pentagonal prism is 648 square inches