Question

In figure, if the area of square $ABCD$ is $5$, calculate the area of square $BEFD$.

• A. $7.07$
• B. $8.25$
• C. $10.00$
• D. $12.50$
• E. $25.00$

Answer 1

Answer: (C)

$10.00$

Given, the area of square $ABCD$ is $5$

Then side of $ABCD$ square $=$ $\sqrt{5}$

The side of square $BDEF$ is the hyptenuse of triangle $BCD$

Then side $BD=$ $\sqrt{(\sqrt{5}{)}^2+(\sqrt{5}{)}^2}=\sqrt{5+5}=\sqrt{10}$

Then area of square $BDEF=$ $($ $\sqrt{10}$ ${)}^2=10$