Answer:
Option A
Step-by-step explanation:
Central angle of the pentagon = [tex]\frac{360}{\text{Number of sides of the regular polygon}}[/tex]
= [tex]\frac{360}{5}[/tex]
= 72°
Measure of ∠BAC = 72°
Therefore, measure of ∠BAD = [tex]\frac{72}{2}[/tex]
= 36°
By sine rule in ΔABD,
sin(36°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{BD}{AB}[/tex]
= [tex]\frac{BD}{14}[/tex]
BD = 14(sin36°)
= 8.23 mm
Similarly, by cosine rule,
cos(36°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{AD}{AB}[/tex]
= [tex]\frac{AD}{14}[/tex]
AD = 14(cos36°)
= 11.33 mm
Area of ΔABC = 2(Area of ΔABD)
= [tex]2(\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= AD × BD
= 11.33 × 8.23
= 93.21 mm²
Since, area of regular pentagon given in the picture = 5(area of ΔABC)
= 5(93.21)
= 466 mm²
Therefore, Option A will be the answer.
