Math / Geometry

QuestionOlfeody Agreteraic Eypresaiens with fxponents - Quat - Levelf
Mr. Donchue is bulding a patio in his bockyard. He wants the patio to cover $\frac{1}{4}$ of the yard. Mr. Donchue wonts to krow the area of the patio. $s=$ length (ft) of one side of the yard.
Which expression shows the area of the patio? $\frac{1}{2} s^{2}$ $\frac{1}{4} x^{2}$ $s^{2}$ $4 s^{2}$

Studdy Solution

STEP 1

1. The yard is a square with side length $s$ .
2. The patio covers $\frac{1}{4}$ of the total area of the yard.

STEP 2

1. Determine the total area of the yard.
2. Calculate the area of the patio as a fraction of the yard's area.
3. Identify the correct expression from the given options.

STEP 3

Determine the total area of the yard:
The area of a square is given by the formula:
$\text{Area of yard} = s^2$

STEP 4

Calculate the area of the patio as a fraction of the yard's area:
Since the patio covers $\frac{1}{4}$ of the yard, the area of the patio is:
$\text{Area of patio} = \frac{1}{4} \times s^2$

STEP 5

Identify the correct expression from the given options:
The expression that represents the area of the patio is:
$\boxed{\frac{1}{4} s^2}$

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