Q. 93.7( 34 Votes )
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm.
Given: AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm
To Find: Area of the quadrilateral
If sides of a triangle are a, b, and c, then area of a triangle is given by:
Where s = semiperimeter of the triangle
Area of a right-angled triangle
AB2 + BC2 = AC2
ABC = 90˚
Therefore, Δ ABC is a right-angled triangle.
∴ Area of Δ ABC = (AB × BC) = 1/2 × 3 × 4 cm2 = 6 cm2
Let 2s be the perimeter of Δ ACD and a = A C = 5 cm, b = CD = 4 cm and c = AD = 5 cm
∴ 2s = a + b+ c 2s = 5 + 4 + 5 s = 7
= 2√21 cm2
∴ Area of quadrilateral ABCD = (6 + 2√21) cm2
Hence, the area of quadrilateral is (6 + 2√21) cm2.
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