Question

If the area of parallelogram $ABCD=70$ sq. units, then the area of $△ABE=$ ___ sq. units.

Answer 1

Let us drop a perpendicular from $E$ to $AB$ extended as shown in the figure. This perpendicular is the height, $h$ of the triangle as well as the parallelogram.

Area of parallelogram $ABCD=$ Base $\times$ Height

Base $=AB$

Height $=h$

$\Rightarrow$ Area $=AB\times h=70$ sq. units ... (i)

Area of $△ABE=\frac{1}{2}\times$ Base $\times$ Height

Base $=AB$

Height $=h$

$\Rightarrow$ Area $=\frac{1}{2}\times AB\times h=\frac{70}{2}=35$ sq. units [Using (i)]

Alternatively,

From the theorem:

If a parallelogram and a triangle are on the same base and between same parallel lines, then the area of the triangle is half the area of the parallelogram.

Given, area of the parallelogram, $ABCD=70$ sq. units

$\Rightarrow$ Area of $△ABE=\frac{1}{2}\times$ area of parallelogram $ABCD$

$=\frac{1}{2}\times 70=35$ sq. units