Question

What is the ratio of the area of parallelogram ABCD to the sum of areas of $\Delta ABE$ and $\Delta ABF?$

• A. 1:2
• B. 1:1
• C. 2:1
• D. 1:3

Answer 1

The correct option is B

1:1

We can clearly see that

EG = DH = FI --------- (1)

So, the height of the parallelogram ABCD is exactly equal to the heights of $\Delta ABE$ and $\Delta ABF$.

Also, the base of all the figures is the same i.e. AB.

Area of a parallelogram $=base\times height$

Area of parallelogram $ABCD=AB\times DH$

Area of a $\Delta =\frac{1}{2}\times base\times height$

Area of $\Delta ABE=\frac{1}{2}\times AB\times EG$

Area of $\Delta ABF=\frac{1}{2}\times AB\times FI$

Area of $\Delta ABE+Areaof\Delta ABF=[\frac{1}{2}\times AB\times EG)]+[\frac{1}{2}\times AB\times FI]$

$=AB\times DH$ [Using equation 1]

Area of $\Delta ABE$ + Area of $\Delta ABF$ = Area of parallelogram ABCD

Hence, ratio = 1:1