Question

Find the area of the shaded region given that AC is the diameter of the semicircle on AC and BC is the radius of quadrant.​

Answer 1

Answer:

428.6 cm²

Step-by-step explanation:

Since in the given figure, our aim tis to find the area of shaded region if AC is the diameter of semicircle on AC and BC is the radius of quadrant and BC=21& BD = 28​.

The area of the shaded region is equal to the Area of Semi-circle plus the Area of triangle ABC minus the Area of quarter circle.

Thus:

Area of triangle = 1/2 x 21 x 28 = 294 cm²

Then in order to find area of semi-circle, we need to compute:

AC² = 28² + 21²

      = 1225

⇒ AC = 35

The radius of semi-circle is equal to 35/2 = 17.5

Then, we can conclude that the Area is equal to

1/2 x 3.14 x (17.5)² = 480.8 cm²

Thus the Area of quarter circle is equal to:

1/4 x 3.14 x 21²= 346.2 cm²

Area of shaded region = 294 + 480.8 - 346.2 = 428.6 cm²

Hence, our area is equal to 428.6 cm².