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.

Answer :

Given: AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm, and AC = 5 cm

To Find: Area of the quadrilateral


Concept Used:


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


Diagram:



Explanation:


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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