Question

find the area of the polygon​

Answer 1

Calculating the area of triangle PQR:

$Area \: of \: Triangle \: PQR = \frac{b \times h}{2}$

$= \frac{10 \times 5}{2}$

$= \frac{50}{2}$

$= 25 \: {cm}^{2}$

Calculating the area of Trapezium PTSR:

$Area \: of \: Trapezium \: PTSR \: = \frac{h(a + b)}{2}$

$= \frac{4(6 + 10)}{2}$

$= 2(6 + 10)$

$= 2 \times 16$

$= 32 \: {cm}^{2}$

The total area of the Polygon is Area of Triangle + Area of Trapezium.

$= 25 + 32$

$= 57 \: {cm}^{2}$

Hope this helps.

Thanks.

Answer 2

ANSWER :-

• Area of Polygon = 57 cm²

GIVEN :-

❂ In figure PQRST,

⇰ PR = 10 cm

⇰ TU = 4 cm

⇰ ST = 6 cm

⇰ QV = 5 cm

SOLUTION :-

❂ Area of △ PQR ,

↣ 1/2 (PR × QV)

↣ 1/2 (10 cm × 5 cm)

↣ 5 × 5 cm²

↣ 25 cm².

❂ Area of △ PQR = 25 cm²

❂ Area of ⏢ PRST ,

⇢ 1/2 (PR + ST) × TU

⇢ 1/2 (10 cm + 6 cm) × 4 cm

⇢ 16 cm × 2 cm

⇢ 32 cm²

❂ Area of ⏢ PRST = 32 cm².

Hence we found,

⇰ Area of △ PQR = 25 cm²

⇰ Area of ⏢ PRST = 32 cm²

❂ Area of Polygon PQRST,

⟾ Area (triangle) + Area (trapezium)

⟾ 25 cm² + 32 cm²

⟾ 57 cm²

Hence the Area of Polygon is 57 cm².