Question

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.

Solution

For ΔABC
a = 4 cm
b = 5 cm
c = 3 cm
∵ a² + c² = b²

∴ ΔABC is right angled with ∠B = 90°.
∴ Area of right triangle ABC
$equals 1 half cross times space Base space cross times space Height equals space 1 half cross times 3 cross times 4 equals 6 space cm squared$

For ΔACD
a = 4 cm b = 5 cm
c = 5 cm
$therefore space space space space space space space straight s space equals space fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space space space space space space space space space space space equals space fraction numerator 4 plus 5 plus 5 over denominator 2 end fraction equals 14 over 2 equals 7 space cm$
∴ Area of the ΔACD
$equals space square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals space square root of 7 left parenthesis 7 minus 4 right parenthesis left parenthesis 7 minus 5 right parenthesis left parenthesis 7 minus 5 right parenthesis end root equals space square root of 7 left parenthesis 3 right parenthesis left parenthesis 2 right parenthesis left parenthesis 2 right parenthesis end root equals 2 square root of 21 space cm squared$

= 2 x 4.6 cm² (approx.)
= 9.2 cm² (approx.)
∴ Area of the quadrilateral ABCD
= Area of ΔABC + Area of ΔACD
= 6 cm² + 9.2 cm²= 15.2 cm², (approx.)

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Statistics

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.

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