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19. A plot of land is in the form of a quadrilateral, one of its diagonals is 320 m long. The two vertices on side of this diagonal are 30 m and 75 m away. Find the area of the plot? |
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Answer» :Given diagonal of a quadrilateral plot = 320 mLet We have a quadrilateral plot ABCD ,HereAC = 320 MAND Distance between AC to VERTEX D = 30 m , So DE = 30 m ( That is also height of ∆ ACD )And Distance between AC to vertex B = 75 m , So FB = 75 m ( That is also height of ∆ ABC )Area of quadrilateral plot ABCD = Area of ∆ ACD + Area of ∆ ABCWe know Area of Triangle = 1/2× Base × HeightSo,Area of ∆ ACD = 1/2× AC × DE = 1/2×320×30 = 160 × 30 = 4800 m2AndArea of ∆ ABC = 1/2× AC × FB = 1/2×320×75 = 160 × 75 = 12000 m2ThenArea of quadrilateral plot ABCD = 4800 + 12000 = 16800 m2 ( Ans ) |
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