To the nearest tenth of square inch, find the area of the regular pentagon whose apothem measures 4.2 inches and whose sides measure 6.2 inches.
A) $64.2 \mathrm { in } ^ { 2 }$
B) $65.1 \mathrm { in } ^ { 2 }$
C) $97.6 \mathrm { in } ^ { 2 }$
D) $130.2 \mathrm { in } ^ { 2 }$

Question

To the nearest tenth of square inch, find the area of the regular pentagon whose apothem  measures 4.2 inches and whose sides measure 6.2 inches.
A) $64.2 \mathrm { in } ^ { 2 }$ 
B) $65.1 \mathrm { in } ^ { 2 }$ 
C) $97.6 \mathrm { in } ^ { 2 }$ 
D) $130.2 \mathrm { in } ^ { 2 }$

Quizplus · Accepted Answer

To find the area of a regular pentagon, we use the formula
$$A = \frac{5}{2}L \cdot A,$$
where $L$ is the length of a side of the pentagon and $A$ is the apothem (the distance from the center of the pentagon to the midpoint of a side). 
Substituting $L = 6.2$ and $A = 4.2$ into the formula, we get
$$A = \frac{5}{2}(6.2)(4.2) \approx 65.1 	ext{ square inches (to the nearest tenth)}.$$ 
Therefore, the answer is B.

To the Nearest Tenth of Square Inch, Find the Area 64.2in264.2 \mathrm { in } ^ { 2 }64.2in2

To the Nearest Tenth of Square Inch, Find the Area $64.2 \mathrm { in } ^ { 2 }$