Question

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

Answer 1

Answer:

313.25

Step-by-step explanation:

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Answer 2

Find the area of the big rectangle:

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

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

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

Find the area of triangle DPQ:

$\text{Base} = 17 - 5$

$\text {Base} = 12 \text{ m}$

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

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

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

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

Find the area of triangle QAR:

$\text{Base} = 25 - 14$

$\text {Base} = 11 \text{ m}$

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

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

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

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

Find the area of triangle PCS:

$\text{Base} = 25 - 8$

$\text {Base} = 17 \text{ m}$

$\text {Height} = 17 - 3$

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

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

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

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

Find the area of triangle RBS:

$\text {Base} = 14 \text{ m}$

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

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

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

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

Find the area of the shaded region:

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

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

Answer: 209.5 m²