Mathematics
In the given figure, M and N are the mid-points of the sides DC and AB respectively of the parallelogram ABCD.
If the area of parallelogram ABCD is 48 cm2;
(i) state the area of the triangle BEC.
(ii) name the parallelogram which is equal in area to the triangle BEC.
Theorems on Area
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Answer
(i) We know that,
Area of a triangle is half that of a parallelogram on the same base and between the same parallels.
Since, triangle BEC and parallelogram ABCD are on the same base BC and between the same parallels AE and BC.
∴ Area of △ BEC = Area of || gm ABCD = = 24 cm2.
Hence, the area of the triangle BEC = 24 cm2.
(ii) Since, M and N are the mid-points of the sides DC and AB respectively.
∴ Area of || gm ANMD = Area of || gm NBCM = Area of || gm ABCD ………(1)
From part (i), we get :
Area of △ BEC = Area of || gm ABCD ……..(2)
From equation (1) and (2), we get :
Area of || gm ANMD = Area of || gm NBCM = Area of △ BEC.
Hence, parallelograms ANMD and NBCM are equal in area to triangle BEC.
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