11. Find the area of the shaded region in Fig. 17.12
12 cm
52 cm
16 cm
48 cm
Fig. 17.12
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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
√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
Therefore, the area of the shaded region is 384 cm².
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