QuestionCompare the area of a rectangle (7 in by $\frac{3}{4}$ in) and a square (side $2 \frac{1}{2}$ in).

Studdy Solution

STEP 1

Assumptions1. The rectangle has a length of7 inches and a width of $\frac{3}{4}$ inch. . The square has a side length of $\frac{1}{}$ inches.
3. The area of a rectangle is calculated by multiplying its length by its width.
4. The area of a square is calculated by squaring its side length.

STEP 2

First, we need to find the area of the rectangle. We can do this by multiplying the length of the rectangle by its width.
$Area_{rectangle} = Length_{rectangle} \\times Width_{rectangle}$

STEP 3

Now, plug in the given values for the length and width of the rectangle to calculate its area.
$Area_{rectangle} =7\, inches \\times \frac{3}{}\, inch$

STEP 4

Calculate the area of the rectangle.
$Area_{rectangle} =7\, inches \\times \frac{3}{4}\, inch = \frac{21}{4}\, square\, inches =.25\, square\, inches$

STEP 5

Next, we need to find the area of the square. We can do this by squaring the side length of the square.
$Area_{square} = Side_{square}^2$

STEP 6

Now, plug in the given value for the side length of the square to calculate its area.
$Area_{square} = \left(2 \frac{1}{2}\, inches\right)^2$

STEP 7

Calculate the area of the square.
$Area_{square} = \left(2 \frac{1}{2}\, inches\right)^2 =6.25\, square\, inches$

STEP 8

Now that we have the areas of both the rectangle and the square, we can compare them to determine which shape has a larger area.
The square with a side length of $2 \frac{1}{2}$ inches has a larger area than the rectangle that is7 inches by $\frac{3}{4}$ inch.

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