Question

find the area of each of the following. 17. square whose sides are 9.1 yd in length 18. square whose sides are (x + 1) in length 19. triangle whose base is 5 1/2 in. and whose height is 2 1/4 in.

Explanation:

Step1: Recall area formula for square

The area formula for a square is $A = s^2$, where $s$ is the side - length.
For the square in problem 17 with $s = 9.1$ yd, we substitute $s$ into the formula.
$A_{17}=(9.1)^2=82.81$ yd²

Step2: Expand the square for problem 18

For the square with $s=(x + 1)$, we use the formula $A=s^2=(x + 1)^2$.
By the formula $(a + b)^2=a^{2}+2ab + b^{2}$, where $a=x$ and $b = 1$, we get $A_{18}=x^{2}+2x + 1$.

Step3: Recall area formula for triangle

The area formula for a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.
The base $b = 5\frac{1}{2}=\frac{11}{2}$ in and the height $h=2\frac{1}{4}=\frac{9}{4}$ in.
Substitute $b$ and $h$ into the formula: $A_{19}=\frac{1}{2}\times\frac{11}{2}\times\frac{9}{4}=\frac{99}{16}=6\frac{3}{16}$ in²

Answer:

1. $82.81$ yd²
2. $x^{2}+2x + 1$
3. $6\frac{3}{16}$ in²