Question

If pq=15cm and pr=8cm find the area of the shaded region
In the adjacent figure qr is the diameter of the circle with centre O if pq=15cm and pr=8cm find the area of the shaded region

Answer 1

Answer:

The Area of shaded region is 53.43 cm²  .

Step-by-step explanation:

Given as :

The circle with center o

The diameter of circle = QR = d cm

The measure of PR =  8 cm

The measure of PQ = 15 cm

According to question

In triangle PQR

From Pythagoras theorem

QR = $\sqrt{PR^{2} + PQ^{2} }$

Or, QR = $\sqrt{8^{2} + 15^{2} }$

Or, QR = $\sqrt{289}$

∴   QR = 17 cm

Now, Area of Δ PQR = $\dfrac{1}{2}$ × PR × PQ

i.e Area of Δ PQR = $\dfrac{1}{2}$ × 8 × 15

Or, Area of Δ PQR = 60 cm²

Again

Area of semi-circle with radius OQ = r

i.e Radius = $\dfrac{QR}{2}$ = 8.5 cm

Area of semi-circle = $\dfrac{\Pi \times {r}^{2}}{2}$

Or, Area of semi-circle = $\dfrac{3.14\times {8.5}^{2}}{2}$

∴ Area of semi-circle = 113.43 cm²

Area of shaded region = Area of semi-circle -  Area of Δ PQR

Or, Area of shaded region = 113.43 cm² - 60 cm²

Or,  Area of shaded region = 53.43 cm²

Hence, The Area of shaded region is 53.43 cm²  . Answer

Answer 2

The area of the shaded region is $53.43 \ cm^2$

Explanation:

The diameter of the circle is QR

The length of PQ is $15 \ cm$

The length of PR is $8 \ cm$

Using Pythagorean theorem, we shall determine the length of QR,

$\mathrm{QR}=\sqrt{P R^{2}+P Q^{2}}$

$\mathrm{QR}=\sqrt{8^{2}+15^{2}}$

$\mathrm{QR}=\sqrt{289}$

$\mathrm{QR}=17 \mathrm{cm}$

The area of $\triangle PQR$ = $\frac{1}{2} bh$ $=\frac{1}{2} (8)(15)=60 cm^2$

The area of the semi circle is given by

$\frac{1}{2} \pi r^2$ $= \frac{1}{2} (3.14)(8.5)^2$

       $=\frac{1}{2} (3.14)(72.25)$

       $=113.42 \ cm^2$

Now, we shall find the area of the shaded region by subtracting the area of the semi circle and the area of the triangle.

Thus, we have,

Area of the shaded region = Area of the semi circle - Area of the triangle

Substituting the values, we get,

Area of the shaded region = $113.42-60=53.42 \ cm^2$

Hence, the area of the shaded region is $53.43 \ cm^2$

Learn more:

(1) In the adjacent figure, QR is the diameter of the circle with

centre 'O'. If PQ = 15 cm, PR=8 cm, find the area of the

shaded region. (Use r=3.14)

8 cm

15cm

8​

brainly.in/question/15437680

(2) In the adjacent figure QR is the diameter of the circle with centre 'O'. If PQ=15 cm,PR=8 cm , find the area of the shaded region​

brainly.in/question/15568203