Calculate the shaded areas.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for the shaded areas:

1(a)

Calculate the area of the large rectangle.
$A_{\text{large}} = \text{length} \times \text{width} = 7 \text{ cm} \times 4 \text{ cm} = 28 \text{ cm}^{2}$
Calculate the area of the small unshaded rectangle.
$A_{\text{small}} = \text{length} \times \text{width} = 5 \text{ cm} \times 2 \text{ cm} = 10 \text{ cm}^{2}$
Calculate the shaded area by subtracting the small area from the large area.
$A_{\text{shaded}} = A_{\text{large}} - A_{\text{small}} = 28 \text{ cm}^{2} - 10 \text{ cm}^{2} = 18 \text{ cm}^{2}$
The shaded area is $\boxed{18 \text{ cm}^{2}}$ .

1(b)
Identify the overall shape as a square with side length 6.
The unshaded part is a square with side length 3.
Calculate the area of the overall square.
$A_{\text{overall}} = 6 \times 6 = 36$
Calculate the area of the unshaded square.
$A_{\text{unshaded}} = 3 \times 3 = 9$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{overall}} - A_{\text{unshaded}} = 36 - 9 = 27$
The shaded area is $\boxed{27}$ .

2(a)
Calculate the area of the large rectangle.
$A_{\text{large}} = 8 \times 5 = 40$
Calculate the area of the small unshaded rectangle.
$A_{\text{small}} = 5 \times 3 = 15$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{large}} - A_{\text{small}} = 40 - 15 = 25$
The shaded area is $\boxed{25}$ .

2(b)
Calculate the area of the large rectangle.
$A_{\text{large}} = 6 \times 5 = 30$
Calculate the area of the small unshaded rectangle.
$A_{\text{small}} = 3 \times 2 = 6$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{large}} - A_{\text{small}} = 30 - 6 = 24$
The shaded area is $\boxed{24}$ .

3(a)
Calculate the area of the large square.
$A_{\text{square}} = 5 \times 5 = 25$
Calculate the area of the unshaded triangle.
$A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{square}} - A_{\text{triangle}} = 25 - 8 = 17$
The shaded area is $\boxed{17}$ .

3(b)
Assumption: The outer shape is a square with side length 5, and the inner unshaded shape is a rectangle with dimensions 2 by 3.
Calculate the area of the outer square.
$A_{\text{outer}} = 5 \times 5 = 25$
Calculate the area of the inner unshaded rectangle.
$A_{\text{inner}} = 3 \times 2 = 6$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 25 - 6 = 19$
The shaded area is $\boxed{19}$ .

4(a)
Determine the dimensions and calculate the area of the outer square.
The outer width is $4 + 2 = 6$ . The outer height is $2 + 2 + 2 = 6$ .
$A_{\text{outer}} = 6 \times 6 = 36$
Determine the dimensions and calculate the area of the inner unshaded square.
The inner width is 4. The inner height is $2 + 2 = 4$ .
$A_{\text{inner}} = 4 \times 4 = 16$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 36 - 16 = 20$
The shaded area is $\boxed{20}$ .

4(b)
Calculate the area of the outer rectangle.
$A_{\text{outer}} = 6 \times 5 = 30$
Calculate the area of the inner unshaded rectangle.
$A_{\text{inner}} = 3 \times 2 = 6$
Calculate the shaded area.
$A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} = 30 - 6 = 24$
The shaded area is $\boxed{24}$ .

Calculate the shaded areas.

Step-by-step solution

Calculate the area of the large rectangle.

Calculate the area of the small unshaded rectangle.

Calculate the shaded area by subtracting the small area from the large area.

Identify the overall shape as a square with side length 6.

Calculate the area of the overall square.

Calculate the area of the unshaded square.

Calculate the shaded area.

Calculate the area of the large rectangle.

Calculate the area of the small unshaded rectangle.

Calculate the shaded area.

Calculate the area of the large rectangle.

Calculate the area of the small unshaded rectangle.

Calculate the shaded area.

Calculate the area of the large square.

Calculate the area of the unshaded triangle.

Calculate the shaded area.

Calculate the area of the outer square.

Calculate the area of the inner unshaded rectangle.

Calculate the shaded area.

Determine the dimensions and calculate the area of the outer square.

Determine the dimensions and calculate the area of the inner unshaded square.

Calculate the shaded area.

Calculate the area of the outer rectangle.

Calculate the area of the inner unshaded rectangle.

Calculate the shaded area.

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