Question

2. In the figure, AB = 25 m, AD = 17 m, DP = 8 m, AQ = 5 m, BR = 14 m and
BS = 3 m. Find the area of the shaded region.​

Answer 1

Step-by-step explanation:

Find the area of the big rectangle:

\text{Area} = \text{Length} \times \text{Breadth}Area=Length×Breadth

\text{Area} = \text{25} \times \text{17}Area=25×17

\text{Area} = 425 \text{ m}^2Area=425 m2

Find the area of triangle DPQ:

\text{Base} = 17 - 5Base=17−5

\text {Base} = 12 \text{ m}Base=12 m

\text {Height} = 8 \text{ m}Height=8 m

\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}Area of triangle=21×Base×Height

\text{Area of triangle} = \dfrac{1}{2} \times \text{12} \times \text{8}Area of triangle=21×12×8

\text{Area of triangle} = 48 \text{ m}^2Area of triangle=48 m2

Find the area of triangle QAR:

\text{Base} = 25 - 14Base=25−14

\text {Base} = 11 \text{ m}Base=11 m

\text {Height} = 5 \text{ m}Height=5 m

\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}Area of triangle=21×Base×Height

\text{Area of triangle} = \dfrac{1}{2} \times \text{11} \times \text{5}Area of triangle=21×11×5

\text{Area of triangle} = 27.5 \text{ m}^2Area of triangle=27.5 m2

Find the area of triangle PCS:

\text{Base} = 25 - 8Base=25−8

\text {Base} = 17 \text{ m}Base=17 m

\text {Height} = 17 - 3Height=17−3

\text {Height} = 14 \text{ m}Height=14 m

\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}Area of triangle=21×Base×Height

\text{Area of triangle} = \dfrac{1}{2} \times \text{17} \times \text{14}Area of triangle=21×17×14

\text{Area of triangle} = 119 \text{ m}^2Area of triangle=119 m2

Find the area of triangle RBS:

\text {Base} = 14 \text{ m}Base=14 m

\text {Height} = 3 \text{ m}Height=3 m

\text{Area of triangle} = \dfrac{1}{2} \times \text{Base} \times \text{Height}Area of triangle=21×Base×Height

\text{Area of triangle} = \dfrac{1}{2} \times \text{14} \times \text{3}Area of triangle=21×14×3

\text{Area of triangle} = 21 \text{ m}^2Area of triangle=21 m2

Find the area of the shaded region:

\text{Shaded Region} = 425 - 48 - 27.5 - 119 - 21Shaded Region=425−48−27.5−119−21

\text{Shaded Region} = 209.5 \text { m}^2Shaded Region=209.5 m2

Answer: 209.5 m²