Question

Determine the area of a regular pentagon that has a perimeter of 22 cm in the apothem of 3 cm

Answer 1

165

Step-by-step explanation:

The formula for the area of the pentagon is 5/2 × s × a.

5/2×22×3

5/2 × 66/1= 66÷2

=33

33×5=165

Answer 2

Answer: 33 square cm

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Step-by-step explanation:

Refer to the diagram below. I've split the regular pentagon into 5 equal slices (as if it was a pizza). Each triangle is congruent.

The base of each triangle is 22/5 = 4.4 cm

The height of each triangle is the apothem 3 cm. The apothem stretches from the center to the midpoint of any given side. It's the red dashed line in the diagram.

The area of one of the triangles is base*height/2 = 4.4*3/2 = 6.6 square cm.

Since we have 5 identical triangles with this area, we have a total area of 5*6.6 = 33 square cm