Question

a model of a soccer ball is made up of regular pentagons and hexagons.
the side length of one of the pentagons measures 2 inches and the apothem measures about 1.38 inches.
what is the area of one of the pentagons? state your answer to the nearest tenth.
$\boldsymbol{square}$ square inches
the side length of one of the hexagons measures 2 inches and the apothem measures about 1.73 inches.
what is the area of one of the hexagons? state your answer to the nearest tenth.
$\boldsymbol{square}$ square inches

Explanation:

Step1: Find pentagon perimeter

$P_{\text{pentagon}} = 5 \times 2 = 10$ inches

Step2: Calculate pentagon area

Use formula $A=\frac{1}{2} \times a \times P$
$A_{\text{pentagon}} = \frac{1}{2} \times 1.38 \times 10 = 6.9$ square inches

Step3: Find hexagon perimeter

$P_{\text{hexagon}} = 6 \times 2 = 12$ inches

Step4: Calculate hexagon area

Use formula $A=\frac{1}{2} \times a \times P$
$A_{\text{hexagon}} = \frac{1}{2} \times 1.73 \times 12 = 10.38 \approx 10.4$ square inches

Answer:

Area of one pentagon: 6.9 square inches
Area of one hexagon: 10.4 square inches