Question

In a rectangular field of dimensions 60m X 50m, a triangular park is constructed. If the dimensions of the park is 51m , 37m and 20 m , find the area of the remaining field.
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Answer 1

Answer:

area of rectangle- area of triangle = area of remaining field

now 60 × 50 - area of triangle by herone formula = area of remaining field

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Answer 2

↛ Area of rectangular field = length × breadth

= 60 × 50 = 3000msq.

✯ Now, a = 51m, b = 37m, c = 20m

$S = \frac{a + b + c}{2}$

$\frac{51 + 37 + 20}{2} = \cancel\frac{108}{2} = 54m$

✯ By Heron's formula :

$∴ \sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{54(54 - 51)(54 - 37)(54 - 20)}$

$\sqrt{54 \times 3 \times 17 \times 34}$

$= 93636m {}^{2}$

✯ Hence, the remaining area = Area of rectangle - Area of traingle

→ 3000 - 93636 = 90636msq.

$\boxed {\purple{Remaining \: area = 90636m {}^{2}}}$