Answer:
15.25 cm²
Step-by-step explanation:
Step 1: find the width of the rectangle, AE.
[tex] cos(60) = \frac{EA}{8} [/tex]
[tex] 8*0.5 = EA [/tex]
[tex] 4 = EA [/tex]
[tex] EA = 4 cm [/tex]
Step 2: Find the area of the rectangle
[tex] Area_{rectangle} = length * width = 8*4 = 32 cm^2 [/tex]
Step 3: Find the area of the sector.
Take π as 3.14
[tex] Area_{sector} = \frac{30}{360}*3.14*8^2 [/tex]
[tex] Area_{sector} = \frac{30}{360}*3.14*8^2 = 16.75 cm^2 [/tex]
Step 4: Find the area of the shaded region.
Area of shaded region = [tex] Area_{Rectangle} - Area_{sector} = 32 - 16.75 = 15.25 cm^2 [/tex]
