QuestionFind the area of a square with a side length of 12 yards in square feet. Show two methods to calculate it.

Studdy Solution

STEP 1

Assumptions1. The side length of the square is12 yards. . We need to convert the area from square yards to square feet. 3.1 yard is equal to3 feet.
Method1 Find the area in square yards first, then convert to square feet.

STEP 2

First, we need to find the area of the square in square yards. The formula for the area of a square is side length squared.
$Area_{yards} = Side\, length^2$

STEP 3

Now, plug in the given value for the side length to calculate the area in square yards.
$Area_{yards} =12\, yards^2$

STEP 4

Calculate the area in square yards.
$Area_{yards} =12\, yards \times12\, yards =144\, square\, yards$

STEP 5

Now, we need to convert the area from square yards to square feet. We know that1 yard is equal to3 feet, so1 square yard is equal to9 square feet.
$Area_{feet} = Area_{yards} \times9$

STEP 6

Plug in the value for the area in square yards to calculate the area in square feet.
$Area_{feet} =144\, square\, yards \times9$

STEP 7

Calculate the area in square feet.
$Area_{feet} =144\, square\, yards \times9 =1296\, square\, feet$ Method2 Convert the side length to feet first, then find the area.

STEP 8

First, we need to convert the side length from yards to feet. We know that1 yard is equal to3 feet.
$Side\, length_{feet} = Side\, length_{yards} \times3$

STEP 9

Plug in the given value for the side length to calculate the side length in feet.
$Side\, length_{feet} =12\, yards \times3$

STEP 10

Calculate the side length in feet.
$Side\, length_{feet} =12\, yards \times3 =36\, feet$

STEP 11

Now, we need to find the area of the square in square feet. The formula for the area of a square is side length squared.
Area_{feet} = Side\, length_{feet}^

STEP 12

Plug in the value for the side length in feet to calculate the area in square feet.
$Area_{feet} =36\, feet^2$

STEP 13

Calculate the area in square feet.
$Area_{feet} =36\, feet \times36\, feet =1296\, square\, feet$ The area of the square is1296 square feet.

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