Question

find the area of the above figure​

Answer 1

Answer:

$75 {cm}^{2}$

Step-by-step explanation:

$area \: of \: triangle = \frac{1}{2} \: base \: \times height \\ = \: \: \: \: \: \: = \frac{1}{2} \times 14 \times 15 \\ \: \: \: \: \: \: = 7 \times 15 \\ \: \: \: \: \: \: = 105cm ^{2} \\ area \: of \: unshaded \: region = \frac{1}{2} \times 12 \times 5 \\ \: \: \: \: \: \: = 6 \times 5 \\ \: \: \: \: \: \: \: = 30 {cm}^{2} \\ \: \: \: \: \: \: area \: of \: shaded \: region = area \: of \: triangle - area \: of \: unshaded \: region \\ \: \: \: \: \: = 105 - 30 \\ \: \: \: \: \: = 75 {cm}^{2}$

Answer 2

Area of shaded region = Area of ∆ABC - Area of ∆ABD

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∆ABD is a right triangle, hence the area is

$\frac{1}{2} \times b \: \times h$

b = 5cm

h = 12cm

---> Area = 1/2 x 5 x 12

---> Area = 5 x 6

---> Area = 30cm^2

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Also, In ∆ABC,

AB^2 = AD^2 + DB^2

AB^2 = 12^2 + 5^2

AB^2 = 144 + 25

AB^2 = 169

AB = √169

AB = 13cm

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$area \: of \: \triangle \: abc \: = \sqrt{s(s - a)(s - b)(s - c)}$

Here,

s = a + b + c/2

= 13 + 14 + 15/2

= 42/2

= 21

•a = 13

•b = 14

•c = 15

substituting the values in the formula,

$area \: = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} \\ = > \sqrt{21(8)(7)(6)} \\ = > \sqrt{7056} \\ = > 84{cm}^{2}$

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Area of shaded region = 84 - 30

= 54cm^2