Mathematics: The diagram shows a rectangle ABCE. D lies on EC.DAB is a sector of a circle radius 8cm and sector angle 30º.Calculate the area of the shaded region.

37 Step-by-step explanation:...

The diagram shows a rectangle ABCE. D lies on EC.DAB

chloebaby8

31.01.2022

15.25 cm²

Step-by-step explanation:

Step 1: find the width of the rectangle, AE.

$cos(60) = \frac{EA}{8}$

8*0.5 = EA

4 = EA

EA = 4 cm

Step 2: Find the area of the rectangle

$Area_{rectangle} = length * width = 8*4 = 32 cm^2$

Step 3: Find the area of the sector.

Take π as 3.14

$Area_{sector} = \frac{30}{360}*3.14*8^2$

$Area_{sector} = \frac{30}{360}*3.14*8^2 = 16.75 cm^2$

Step 4: Find the area of the shaded region.

Area of shaded region = $Area_{Rectangle} - Area_{sector} = 32 - 16.75 = 15.25 cm^2$

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