Math  /  Geometry

QuestionA rectangular region is removed from another rectangular region to create the shaded regions shown below. Find the combined area of the shaded regions. \square ft2\mathrm{ft}^{2}

Studdy Solution

STEP 1

1. The large rectangle has dimensions of 7 7 ft by 14 14 ft.
2. The smaller rectangle removed from the top right corner has dimensions of 3 3 ft by 7 7 ft.
3. The shaded regions are the areas of the large rectangle not occupied by the smaller rectangle.

STEP 2

1. Calculate the area of the large rectangle.
2. Calculate the area of the smaller rectangle.
3. Subtract the area of the smaller rectangle from the area of the large rectangle to find the combined area of the shaded regions.

STEP 3

Calculate the area of the large rectangle using the formula for the area of a rectangle:
Arealarge=Length×Width \text{Area}_{\text{large}} = \text{Length} \times \text{Width} =14 ft×7 ft = 14 \text{ ft} \times 7 \text{ ft}
Arealarge=98 ft2 \text{Area}_{\text{large}} = 98 \text{ ft}^2

STEP 4

Calculate the area of the smaller rectangle using the formula for the area of a rectangle:
Areasmall=Length×Width \text{Area}_{\text{small}} = \text{Length} \times \text{Width} =7 ft×3 ft = 7 \text{ ft} \times 3 \text{ ft}
Areasmall=21 ft2 \text{Area}_{\text{small}} = 21 \text{ ft}^2

STEP 5

Subtract the area of the smaller rectangle from the area of the large rectangle to find the combined area of the shaded regions:
Areashaded=ArealargeAreasmall \text{Area}_{\text{shaded}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} =98 ft221 ft2 = 98 \text{ ft}^2 - 21 \text{ ft}^2
Areashaded=77 ft2 \text{Area}_{\text{shaded}} = 77 \text{ ft}^2
The combined area of the shaded regions is:
77 ft2 \boxed{77 \text{ ft}^2}

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