Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
Answers
Given : Quadrilateral ABCD with AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm & diagonal AC = 5 cm.
To Find : area of ∆ ABC and ∆ADC
In ΔABC,
By applying Pythagoras Theorem
AC² = AB² + BC²
5² = 3² + 4²
25 = 25
Thus, ΔABC is a right-angled at B.
Area of ΔBCD = ½ × base × height.
Area of ΔBCD = 1/2 × 3 × 4 = 6 cm²
Now,
Semi perimeter of Δ (s) = (a + b + c)/2
Semi perimeter of ΔACD(s) = (5 + 5 + 4)/2
s = 14/2 cm
s = 7 cm
Using heron’s formula :
Area of ΔABD = √s (s - a) (s - b) (s - c)
= √7(7 – 5) (7 – 5) (7 – 4)
= √7 × 2 × 2 × 3
= 2√21cm². (√21 = 4.58)
= 2 × 4.58
Area of ΔABD = 9.16 cm² (approx)
Area of quadrilateral ABCD = Area of ΔABC + Area of ΔABD
Area of quadrilateral ABCD = 6 + 9.16 = 15.16 cm²
Hence, the Area of quadrilateral ABCD is 15.16 cm²
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