Question

PQ = 6 cm Find shaded Portion Area (V3 =1.73,
PR=12 cm
* 3.14​

Answer 1

Step-by-step explanation:

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Answer 2

The area of the shaded portion is 12.33 cm²

Explanation:

Given that PQ = 6 cm and PR = 12 cm

The length of QR:

Using the Pythagorean theorem, we have,

$P R^{2}=P Q^{2}+Q R^{2}$

Substituting the values and simplifying, we get,

  $12^2=6^2+QR^2$

  $144=36+QR^2$

$\sqrt{108}=QR$

$10.39=QR$

Thus, the length of QR is 10.39 cm

Area of ΔPQR:

The formula to determine the area of triangle is given by

$Area = \frac{1}{2}bh$

where b = 10.39 and h = 6

Substituting the values, we have,

$Area=\frac{1}{2}(10.39)(6)$

$Area = 31.17 \ cm^2$

Therefore, the area of the ΔPQR is 31.17 cm²

Area of the sector TPQ:

The formula to determine the area of the sector is given by

$Area=\frac{\theta}{360} \times \pi r^2$

Substituting the values, we have,

$Area=\frac{60}{360} \times (3.14)(6)^2$

$Area=\frac{1}{6} \times (3.14)(36)$

$Area=18.84 \ cm^2$

Thus, the area of the sector TPQ is 18.84 cm²

Area of the shaded region:

The area of the shaded region is given by

Area of the shaded region = Area of the ΔPQR - Area of the sector TPQ

                                            = 31.17 - 18.84

Area of the shaded region = 12.33 cm²

Thus, the area of the shaded region is 12.33 cm²

Learn more:

(1) Find the area of the shaded portion

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(2) Find the area of shaded portion

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