Answered

Calculate the area of the regular pentagon below:


A regular pentagon with side length of 17.6 inches and dotted line from center to middle of side of 12.1 inches.


106.48 square inches

366.025 square inches

451.78 square inches

532.4 square inches

Verified Answer :

taskmasters

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 = (16.88*309.76in²)/4
A = 2131.15 / 4
A = 532.79 in²  

Hippalectryon

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 \(10*\frac{17.6*12.1}4=\boxed{532.4\text{ in}}\)


View image Hippalectryon