11. Find the area of the shaded region in Fig. 17.12
Answers
Answer:
Since ∆ADB is right angled triangle
so, AB = √(12^ + 16^) = 20cm
now,
S = 60
area of ∆ABC = 480cm^2 ( by heron's formula)
area of ∆ADB = 96cm^2
area of shaded region = ( ar∆ABC) – (ar∆ADC) = (480 - 96) cm^2 = 384 cm^2__ans
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11. Find the area of the shaded region in Fig. 17.12
12 cm
52 cm
16 cm
48 cm
Fig. 17.12
Ask for details Follow Report by Ahiri87 01.05.2019
Answers
Swetha02
Swetha02 Ace
We know that Δ ADB is a right angled triangle.
According to the Pythagoras theorem, the area of the square on the hypotenuse is equal to the sum of the areas of the squares of its remaining two sides.
Formula: AD² + DB² = AB² {substituting the values}
12² + 16² = AB²
144 + 256 = AB²
400 = AB²
√400 = AB
AB = 20 cm
Area of ΔADB = √s(s-a)(s-b)(s-c)
s = \frac{12+16+20}{2}cm
s = \frac{48}{2}cm
s = 24cm
a = 12cm
b = 16cm
c = 20cm
√s(s-a)(s-b)(s-c)
√24(24-12)(24-16)(24-20) cm²
√24(12)(8)(4) cm²
√9216 cm²
96 cm²
Area of ΔABD = 96 cm²
Area of ΔABC = √s(s-a)(s-b)(s-c)
s = \frac{52+48+20}{2}cm
s = \frac{120}{2}cm
s = 60cm
a = 52cm
b = 48cm
c = 20cm
√s(s-a)(s-b)(s-c)
√60(60-52)(60-48)(60-20) cm²
√60(8)(12)(40) cm²
√230400 cm²
480 cm²
Area of ΔABC = 480 cm²
Area of the shaded region (quadrilateral ACBD) = Area of ΔABC - Area of ΔABD
Area of quadrilateral ACBD = 480 cm² - 96 cm²
Area of quadrilateral ACBD = 384 cm²