Question

Find the area of the shaded region where O is the center of the circle​

Answer 1

Answer:

471.22 cm²

Step-by-step explanation:

Given -

Shaded Trapezium, with dimensions,

Parallel line 1 (a) = 23 cm (18 cm + 5 cm)

Parallel line 2 (b) = 34 cm

Height (h) = 21 cm

Unshaded Semicircle in the trapezium,

diameter of semicircle = 18 cm

To find -

The total area of shaded region

Solution -

First we have to find the area of trapezium then area of semicircle, then subtract them

Area of trapezium =

$\frac{(a + b)}{2} \times h \\ = \frac{(23 + 34)}{2} \times 21 \: {cm}^{2} \\ = 28.5 \times 21 {cm}^{2} \\ = 598.5 {cm}^{2}$

Now area of semicircle =

$\frac{\pi {r}^{2} }{2}$

Radius = d/2 = 18/2 = 9 cm

$\frac{22}{7} \times \frac{ {9}^{2} }{2 } {cm}^{2} \\ = \frac{22 \times 81}{14} {cm}^{2} \\ = \frac{1782}{14} {cm}^{2} \\ = 127.28 {cm}^{2}$

Here area of semicircle = 127.28 cm² (approx)

So total shaded area = area of trapezium - area of semicircle

= 598.5 cm² - 127.28 cm²

= 471.22 cm²

Hence area of shaded region = 471.22 cm²

Hope it helps.

Answer 2

Answer :-

→ Shaded area = Area of Trapezium ABCE - Area of semi - circle with diameter 18 cm .

we know that,

• Area of trapezium = (1/2)[sum of parallel sides] * height
• Area of semicircle = (1/2)πr²
• Radius = diameter/2 .

so,

→ shaded area = (1/2)[34 + 5 + 18]*21 - (1/2)π*(9)²

→ shaded area = (1/2)[57 * 21 - 3.14 * 81]

→ shaded area = (1/2)[1197 - 254.34]

→ shaded area = (1/2) * 942.66

→ shaded area = 471.33 cm² (Ans.)

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