Question

find the area of shaded region in the figure below​

Answer 1

Step-by-step explanation:

1st we calculate the area of triangle ABC

we kbow that area of tringle=1÷2×base×height

1÷2×16×52=416 cm square

2.Now we calulate the area of ABD triangle

1÷2×12×16=96 cm square

area of shaded region=416-96=320 cm square.

Answer 2

$by \: baudhyan \: theorem$

(AB)² = (AD)²+(BD)²

(AB)²= (12)² + (16)²

(AB)²= 144+ 256=400 = (20)²

on comparing

AB= 20 cm

area of (∆ADB)

$= \frac{1}{2} \times 12 \times 16 = 96cm^{2}$

for area of ∆ABC ,

we will apply heron's formula

$s = \frac{a + b + c}{2} \\ s = \frac{20 + 48 + 52}{2} = 60cm$

we know that,

$area = \sqrt{s(s - a)(s - b)(s - c)} \\ by \: substuting \\ area = \sqrt{60(60 - 20)(60 - 48)(60 - 52)}$

$area = \sqrt{60 \times 40 \times 12 \times 8 } \\ it \: can \: be \: written \: as \: \\ area = \sqrt{12 \times 5 \times 8 \times 5 \times 12 \times 8} \\ after \: calculation \\ area = 12 \times 5 \times 8 = 480 {cm}^{2}$

area of the shaded region =ar(∆ABC)-ar(∆ADB)

480 -36 = 384cm².

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