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Heron’s Formula
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22/07/2021 11:05 am
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A park, in the shape of a quadrilateral ABCD, has C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
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22/07/2021 11:08 am
First, construct a quadrilateral ABCD and join BD.
We know that
C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m
The diagram is:
Now, apply Pythagoras theorem in ΔBCD
BD2 = BC2 + CD2
⇒ BD2 = 122 + 52
⇒ BD2 = 169
⇒ BD = 13 m
Now, the area of ΔBCD = (1/2 × 12 × 5) = 30 m2
The semi perimeter of ΔABD
(s) = (perimeter/2)
= (8 + 9 + 13)/2 m
= 30/2 m = 15 m
Using Heron’s formula,
Area of ΔABD
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{15(15 - 13)(15 - 9)(15 - 8)}m^2\)
= \(\sqrt{15 \times 2 \times 6 \times 7}m^2\)
= 6\(\sqrt{35}m^2\)
= 35.5 m2
∴ The area of quadrilateral ABCD = Area of ΔBCD+Area of ΔABD
= 30 m2 + 35.5m2 = 65.5 m2
This post was modified 3 years ago 2 times by Samar shah