Solved on Aug 22, 2023

Determine the area of the remaining part of a $20 \, \text{ft} \times 15 \, \text{ft}$ flag after a $10 \, \text{ft} \times 14 \, \text{ft}$ triangle is cut from the center.

STEP 1

Assumptions1. The flag is a rectangle with length $20 \, \text{ft}$ and width $15 \, \text{ft}$ . . A triangle is cut out from the center of the flag.
3. The triangle has a base of $10 \, \text{ft}$ and a height of $14 \, \text{ft}$ .
4. The area of the remaining part of the flag is the area of the flag minus the area of the triangle.

STEP 2

First, we need to find the area of the flag. The area of a rectangle is given by the formula $Area_{rectangle} = length \\times width$

STEP 3

Now, plug in the given values for the length and width of the flag to calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft}$

STEP 4

Calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft} =300 \, \text{ft}^2$

STEP 5

Next, we need to find the area of the triangle. The area of a triangle is given by the formula $Area_{triangle} = \frac{1}{2} \\times base \\times height$

STEP 6

Now, plug in the given values for the base and height of the triangle to calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft}$

STEP 7

Calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft} =70 \, \text{ft}^2$

STEP 8

Now that we have the areas of the flag and the triangle, we can find the area of the remaining part of the flag by subtracting the area of the triangle from the area of the flag.
$Area_{remaining} = Area_{flag} - Area_{triangle}$

STEP 9

Plug in the values for the area of the flag and the area of the triangle to calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2$

STEP 10

Calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2 =230 \, \text{ft}^2$ The area of the remaining part of the flag is $230 \, \text{ft}^2$ .

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Determine the area of the remaining part of a $20 \, \text{ft} \times 15 \, \text{ft}$ flag after a $10 \, \text{ft} \times 14 \, \text{ft}$ triangle is cut from the center.

STEP 1

STEP 2

First, we need to find the area of the flag. The area of a rectangle is given by the formula $Area_{rectangle} = length \\times width$

STEP 3

Now, plug in the given values for the length and width of the flag to calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft}$

STEP 4

Calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft} =300 \, \text{ft}^2$

STEP 5

Next, we need to find the area of the triangle. The area of a triangle is given by the formula $Area_{triangle} = \frac{1}{2} \\times base \\times height$

STEP 6

Now, plug in the given values for the base and height of the triangle to calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft}$

STEP 7

Calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft} =70 \, \text{ft}^2$

STEP 8

Now that we have the areas of the flag and the triangle, we can find the area of the remaining part of the flag by subtracting the area of the triangle from the area of the flag.
$Area_{remaining} = Area_{flag} - Area_{triangle}$

STEP 9

Plug in the values for the area of the flag and the area of the triangle to calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2$

STEP 10

Calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2 =230 \, \text{ft}^2$ The area of the remaining part of the flag is $230 \, \text{ft}^2$ .

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Determine the area of the remaining part of a 20 ft×15 ft20 \, \text{ft} \times 15 \, \text{ft}20ft×15ft flag after a 10 ft×14 ft10 \, \text{ft} \times 14 \, \text{ft}10ft×14ft triangle is cut from the center.

STEP 1

STEP 2

First, we need to find the area of the flag. The area of a rectangle is given by the formulaArearectangle=lengthtimeswidthArea_{rectangle} = length \\times widthArearectangle​=lengthtimeswidth

STEP 3

Now, plug in the given values for the length and width of the flag to calculate the area of the flag.Areaflag=20 fttimes15 ftArea_{flag} =20 \, \text{ft} \\times15 \, \text{ft}Areaflag​=20fttimes15ft

STEP 4

Calculate the area of the flag.Areaflag=20 fttimes15 ft=300 ft2Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft} =300 \, \text{ft}^2Areaflag​=20fttimes15ft=300ft2

STEP 5

Next, we need to find the area of the triangle. The area of a triangle is given by the formulaAreatriangle=12timesbasetimesheightArea_{triangle} = \frac{1}{2} \\times base \\times heightAreatriangle​=21​timesbasetimesheight

STEP 6

Now, plug in the given values for the base and height of the triangle to calculate the area of the triangle.Areatriangle=12times10 fttimes14 ftArea_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft}Areatriangle​=21​times10fttimes14ft

STEP 7

Calculate the area of the triangle.Areatriangle=12times10 fttimes14 ft=70 ft2Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft} =70 \, \text{ft}^2Areatriangle​=21​times10fttimes14ft=70ft2

STEP 8

STEP 9

Plug in the values for the area of the flag and the area of the triangle to calculate the area of the remaining part of the flag.Arearemaining=300 ft2−70 ft2Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2Arearemaining​=300ft2−70ft2

STEP 10

Calculate the area of the remaining part of the flag.Arearemaining=300 ft2−70 ft2=230 ft2Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2 =230 \, \text{ft}^2Arearemaining​=300ft2−70ft2=230ft2The area of the remaining part of the flag is 230 ft2230 \, \text{ft}^2230ft2.

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Determine the area of the remaining part of a $20 \, \text{ft} \times 15 \, \text{ft}$ flag after a $10 \, \text{ft} \times 14 \, \text{ft}$ triangle is cut from the center.

First, we need to find the area of the flag. The area of a rectangle is given by the formula $Area_{rectangle} = length \\times width$

Now, plug in the given values for the length and width of the flag to calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft}$

Calculate the area of the flag.
$Area_{flag} =20 \, \text{ft} \\times15 \, \text{ft} =300 \, \text{ft}^2$

Next, we need to find the area of the triangle. The area of a triangle is given by the formula $Area_{triangle} = \frac{1}{2} \\times base \\times height$

Now, plug in the given values for the base and height of the triangle to calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft}$

Calculate the area of the triangle.
$Area_{triangle} = \frac{1}{2} \\times10 \, \text{ft} \\times14 \, \text{ft} =70 \, \text{ft}^2$

Plug in the values for the area of the flag and the area of the triangle to calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2$

Calculate the area of the remaining part of the flag.
$Area_{remaining} =300 \, \text{ft}^2 -70 \, \text{ft}^2 =230 \, \text{ft}^2$ The area of the remaining part of the flag is $230 \, \text{ft}^2$ .