QuestionCalcola la base di un parallelogramma la cui area è $\frac{1}{10}$ di quella di un quadrato di lato $60 \mathrm{~cm}$ e altezza $\frac{1}{4}$ del lato.

Studdy Solution

STEP 1

Assumptions1. The area of the parallelogram is equivalent to $\frac{1}{10}$ of the area of a square with side $60 \mathrm{~cm}$ . . The height of the parallelogram is equal to $\frac{1}{4}$ of the side of the square.

STEP 2

First, we need to calculate the area of the square. The area of a square is given by the formula $Area_{square} = side^2$

STEP 3

Now, plug in the given value for the side of the square to calculate the area.
$Area_{square} =60 \mathrm{~cm}^2$

STEP 4

Calculate the area of the square.
$Area_{square} =60 \mathrm{~cm} \times60 \mathrm{~cm} =3600 \mathrm{~cm}^2$

STEP 5

Now that we have the area of the square, we can find the area of the parallelogram which is $\frac{1}{10}$ of the area of the square.
$Area_{parallelogram} = \frac{1}{10} \times Area_{square}$

STEP 6

Plug in the value for the area of the square to calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2$

STEP 7

Calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2 =360 \mathrm{~cm}^2$

STEP 8

The area of a parallelogram is given by the formula $Area_{parallelogram} = base \times height$ We know the area and the height (which is $\frac{1}{4}$ of the side of the square), so we can solve for the base.
$base = \frac{Area_{parallelogram}}{height}$

STEP 9

Plug in the values for the area of the parallelogram and the height to calculate the base.
$base = \frac{360 \mathrm{~cm}^2}{\frac{}{4} \times60 \mathrm{~cm}}$

STEP 10

Calculate the base of the parallelogram.
$base = \frac{360 \mathrm{~cm}^2}{15 \mathrm{~cm}} =24 \mathrm{~cm}$ The base of the parallelogram is $24 \mathrm{~cm}$ .

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QuestionCalcola la base di un parallelogramma la cui area è $\frac{1}{10}$ di quella di un quadrato di lato $60 \mathrm{~cm}$ e altezza $\frac{1}{4}$ del lato.

Studdy Solution

STEP 1

Assumptions1. The area of the parallelogram is equivalent to $\frac{1}{10}$ of the area of a square with side $60 \mathrm{~cm}$ . . The height of the parallelogram is equal to $\frac{1}{4}$ of the side of the square.

STEP 2

First, we need to calculate the area of the square. The area of a square is given by the formula $Area_{square} = side^2$

STEP 3

Now, plug in the given value for the side of the square to calculate the area.
$Area_{square} =60 \mathrm{~cm}^2$

STEP 4

Calculate the area of the square.
$Area_{square} =60 \mathrm{~cm} \times60 \mathrm{~cm} =3600 \mathrm{~cm}^2$

STEP 5

Now that we have the area of the square, we can find the area of the parallelogram which is $\frac{1}{10}$ of the area of the square.
$Area_{parallelogram} = \frac{1}{10} \times Area_{square}$

STEP 6

Plug in the value for the area of the square to calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2$

STEP 7

Calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2 =360 \mathrm{~cm}^2$

STEP 8

The area of a parallelogram is given by the formula $Area_{parallelogram} = base \times height$ We know the area and the height (which is $\frac{1}{4}$ of the side of the square), so we can solve for the base.
$base = \frac{Area_{parallelogram}}{height}$

STEP 9

Plug in the values for the area of the parallelogram and the height to calculate the base.
$base = \frac{360 \mathrm{~cm}^2}{\frac{}{4} \times60 \mathrm{~cm}}$

STEP 10

Calculate the base of the parallelogram.
$base = \frac{360 \mathrm{~cm}^2}{15 \mathrm{~cm}} =24 \mathrm{~cm}$ The base of the parallelogram is $24 \mathrm{~cm}$ .

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QuestionCalcola la base di un parallelogramma la cui area è 110\frac{1}{10}101​ di quella di un quadrato di lato 60 cm60 \mathrm{~cm}60 cm e altezza 14\frac{1}{4}41​ del lato.

Studdy Solution

STEP 1

Assumptions1. The area of the parallelogram is equivalent to 110\frac{1}{10}101​ of the area of a square with side 60 cm60 \mathrm{~cm}60 cm. . The height of the parallelogram is equal to 14\frac{1}{4}41​ of the side of the square.

STEP 2

First, we need to calculate the area of the square. The area of a square is given by the formulaAreasquare=side2Area_{square} = side^2Areasquare​=side2

STEP 3

Now, plug in the given value for the side of the square to calculate the area.Areasquare=60 cm2Area_{square} =60 \mathrm{~cm}^2Areasquare​=60 cm2

STEP 4

Calculate the area of the square.Areasquare=60 cm×60 cm=3600 cm2Area_{square} =60 \mathrm{~cm} \times60 \mathrm{~cm} =3600 \mathrm{~cm}^2Areasquare​=60 cm×60 cm=3600 cm2

STEP 5

Now that we have the area of the square, we can find the area of the parallelogram which is 110\frac{1}{10}101​ of the area of the square.Areaparallelogram=110×AreasquareArea_{parallelogram} = \frac{1}{10} \times Area_{square}Areaparallelogram​=101​×Areasquare​

STEP 6

Plug in the value for the area of the square to calculate the area of the parallelogram.Areaparallelogram=110×3600 cm2Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2Areaparallelogram​=101​×3600 cm2

STEP 7

Calculate the area of the parallelogram.Areaparallelogram=110×3600 cm2=360 cm2Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2 =360 \mathrm{~cm}^2Areaparallelogram​=101​×3600 cm2=360 cm2

STEP 8

STEP 9

Plug in the values for the area of the parallelogram and the height to calculate the base.base=360 cm24×60 cmbase = \frac{360 \mathrm{~cm}^2}{\frac{}{4} \times60 \mathrm{~cm}}base=4​×60 cm360 cm2​

STEP 10

Calculate the base of the parallelogram.base=360 cm215 cm=24 cmbase = \frac{360 \mathrm{~cm}^2}{15 \mathrm{~cm}} =24 \mathrm{~cm}base=15 cm360 cm2​=24 cmThe base of the parallelogram is 24 cm24 \mathrm{~cm}24 cm.

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QuestionCalcola la base di un parallelogramma la cui area è $\frac{1}{10}$ di quella di un quadrato di lato $60 \mathrm{~cm}$ e altezza $\frac{1}{4}$ del lato.

Assumptions1. The area of the parallelogram is equivalent to $\frac{1}{10}$ of the area of a square with side $60 \mathrm{~cm}$ . . The height of the parallelogram is equal to $\frac{1}{4}$ of the side of the square.

First, we need to calculate the area of the square. The area of a square is given by the formula $Area_{square} = side^2$

Now, plug in the given value for the side of the square to calculate the area.
$Area_{square} =60 \mathrm{~cm}^2$

Calculate the area of the square.
$Area_{square} =60 \mathrm{~cm} \times60 \mathrm{~cm} =3600 \mathrm{~cm}^2$

Now that we have the area of the square, we can find the area of the parallelogram which is $\frac{1}{10}$ of the area of the square.
$Area_{parallelogram} = \frac{1}{10} \times Area_{square}$

Plug in the value for the area of the square to calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2$

Calculate the area of the parallelogram.
$Area_{parallelogram} = \frac{1}{10} \times3600 \mathrm{~cm}^2 =360 \mathrm{~cm}^2$

Plug in the values for the area of the parallelogram and the height to calculate the base.
$base = \frac{360 \mathrm{~cm}^2}{\frac{}{4} \times60 \mathrm{~cm}}$

Calculate the base of the parallelogram.
$base = \frac{360 \mathrm{~cm}^2}{15 \mathrm{~cm}} =24 \mathrm{~cm}$ The base of the parallelogram is $24 \mathrm{~cm}$ .