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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

Respuesta :

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 = (1*6.88*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 [tex]\frac{17.6*12.1}4[/tex]. Hence the total area is [tex]10*\frac{17.6*12.1}4=\boxed{532.4\text{ in}}[/tex]


Ver imagen Hippalectryon

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