Mathematics
In the figure (1) given below, ABCD is a rectangle (not drawn to scale) with side AB = 4 cm and AD = 6 cm. Find
(i) the area of parallelogram DEFC
(ii) area of △EFG.
Theorems on Area
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Answer
(i) We know that,
A parallelogram and a rectangle on the same base and between the same parallel lines are equal in area.
From figure,
rectangle ABCD and parallelogram DEFC are on the same base DC and between same parallel lines DG and AF.
Hence, area of || gm DEFC = area of rectangle ABCD
= AB × AD
= 4 × 6
= 24 cm2.
Hence, area of || gm DEFC = 24 cm2.
(ii) We know that,
Area of a triangle is half that of a parallelogram on the same base and between the same parallel lines.
Since, triangle GEF and || gm DEFC are on same base EF and between same parallel lines DG and AF so,
area of △EFG = area of || gm DEFC
= cm2.
Hence, area of △EFG = 12 cm2.
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