Verified answer

The area of the unshaded region is 218 cm square.

Given:

A figure as shown in the figure above

AB = 12 cm

BP = 16 cm

To Find:

the area of the unshaded region

Solution:

In triangle APB, using the Pythagoras theorem, we can find the value of AB as follows-

AB² = 12² + 16²

AB = √(144 + 256)

AB = √400

AB = 20

Now, the radius of the semi circle will be = 20/2 = 10 cm

the area of the semi-circle will be = π × 10²

= 3.14 × 100

= 314 cm²

The area of the triangle ABP will be = 1/2 × 12 × 16

= 6 × 16

= 96 cm²

Thus, the area of the unshaded region will be = 314 - 96

= 218

Hence, the area of the unshaded region is 218 cm square.

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Answer:

area of unshaded region= 96 cm²

Step-by-step explanation:

As it is a semicircle the angle of APB is 90°

now, area of Δle = 1/2×base ×height

= 1/2×(12×16) cm²

= 96 cm²