Mathematics
In the given figure, the area of △ABC is 64 cm2. State giving reasons:
(i) ar(||gm ABCD)
(ii) ar (rect. ABEF)
Theorems on Area
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Answer
(i) Triangle ABC and a parallelogram ABCD are on the same base AB and between the same parallels AB and CD, then area of triangle is equal to half of the area of the parallelogram.
ar (△ABD) = ar(||gm ABCD)
64 = ar(||gm ABCD)
ar (||gm ABCD) = 64(2)
ar (||gm ABCD) = 128 cm2.
Hence, ar(||gm ABCD) = 128 cm2.
(ii) ||gm ABCD and rectangle ABEF lie on the same base AB and between the same parallels AB and ED.
∴ar (||gm ABCD) = ar (rect. ABEF)
ar (rect. ABEF) = 128 cm2.
Hence, ar(rect. ABEF) = 128 cm2.
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