Question

# Using the measures given in the figure below, find the area of □EFGH.

Solution

## The given map of the plot is of a quadrilateral that can be divided in two triangles, ∆HGF and ∆HEF. Lengths of the sides of ∆HGF are 34 m, 50 m and 52 m Semi-perimeter of a triangle = $s=\frac{a+b+c}{2}$ Semi-perimeter  Area of a triangle =   ∴ Area of the triangle ∆HGF is 816 sq m. Lengths of the sides of the triangle ∆HEF are 20 m, 48 m and 52 m. Semi-perimeter of a triangle = $s=\frac{a+b+c}{2}$ Semi-perimeter = Area of a triangle = ∴ Area of the triangle ∆HEF is 480 sq m. So, the area of $\square EFGH$ = A(∆HGF) + A(∆HEF)                                                      = 816 sq m + 480 sq m =1296 sq mMathematicsMathematics(2013)Standard VIII

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