Chapter A.2, Problem 48AYU

To determine

To find: The area of the triangle $CGF$.

Answer to Problem 48AYU

$64 {\text{ft}}^2$

Explanation of Solution

Given:

Refer to the figure. Square $ABCD$ has an area of 100 square feet; square $BEFG$ has an area of 16 square feet.

Formula Used:

Area of the square $=a^2$ and Area of the triangle $=\frac{1}{2}bh$.

Calculation:

Given, square $ABCD$ has an area of 100 square feet.

Therefore the length of $BC$ is 10 feet, by Area of the square $=a^2={10}^2=100$.

Also given, square $BEFG$ has an area of 16 square feet.

Therefore the length of $BG$ is 4 feet, by Area of the square $=a^2=4^2=16$.

Therefore the length of $GC$ $=$ length of $BC$ $-$ length of $BG$$=16-4=12$ feet.

and the length of $GF$ $=$ length of $BG$ $=4$ feet.

Area of the triangle $=\frac{1}{2}bh=\frac{1}{2}\times 4\times 12=24$.

Given border is square with sides $=6+2\text{ ft = }8\text{ ft}$.

Area of the square $=a^2=8^2=64 {\text{ft}}^2$.