Question

Calculate the area of the regular pentagon below:

Answer 1

Area of the regular pentagon is 532.40 SQUARE INCHES.

Finding the Area of a regular pentagon, use this formula:

A = 1/4 √5(5+2√5) a²

where:  a = side length.

A = 1/4 √5(5+2√5) (17.6in)²
A = 1/4 √5(5+2(2.24) 309.76 in² 
A = 1/4 √5(5+4.48) * 309.76 in²
A = 1/4 √5(9.48) *  309.76 in²
A = 1/4 √47.4 * 309.76 in²
A = 1/4 * 6.88 * 309.76 in²
A = (1*6.88*309.76in²)/4
A = 2131.15 / 4
A = 532.79 in²       

Answer 2

Your pentagon can be decomposed in 10 triangles (see the attached picture). Each triangle has an area $\frac{17.6*12.1}4$. Hence the total area is $10*\frac{17.6*12.1}4=\boxed{532.4\text{ in}}$