in the given figure, ABCD is a field in the the form of quadrilateral whose sides are indicated in the figure. if√DAB=90°,find the area of the field.
Answers
Answer:
Step-by-step explanation:
Area of quadrilateral field abcd = 180 + 126 = 306 m²
Step-by-step explanation:
Area of quadrilateral field abcd = Area of ΔABD + Area of ΔBCD
∠A = 90°
Area of ΔABD = (1/2) * AB * AD = (1/2) 40 * 9 = 180 m²
in ΔABD ∠A = 90°
=> BD² = AB² + AD²
=> BD² = 40² + 9²
=> BD² = 1600 + 81
=> BD² = 1681
=> BD = 41 m
in Δ BCD
BC = 28 m CD = 15 m BD = 41 m
s = (28 + 15 + 41)/2 = 42
Area of Δ BCD = √(42 (42 - 28)(42 - 15)(42 - 41)
= √(42 * 14 * 27 * 1
= √(14 * 3 * 14 * 3 * 3 * 3)
= 14 * 3 * 3
= 126 m²
Area of quadrilateral field abcd = 180 + 126 = 306 m²
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