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Question
The quadrilateral swimming pool shown is surrounded by concrete patio. Find the area of the patio
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Solution
Area of the Quadrilateral ABCD = `1/2[(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (x_2y_1 + x_3y_2 + x_4y_3 + x_1y_4)]`
= `1/2[(16 + 80 + 36 + 80) - (-64 - 24 - 100 - 24)]`
= `1/2[212 - (-212)]`
= `1/2[212 + 212]`
= `1/2[424]`
= 212 sq. units
Area of the Quadrilatera swimming pool EFGH = `1/2[(6 + 42 + 12 + 30) - (- 30 - 6 - 42 - 12)]`
= `1/2[90 - (- 90)]`
= `1/2[90 + 90]`
= `1/2 xx 180`
= 90 sq. units
Area of the patio = Area of the Quadrilateral ABCD – Area of the Quadrilateral EFGH
= (212 – 90) sq. units
Area of the patio = 122 sq. units
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