Question
10
A square with a side length of 5 centimeters is cut out of a square with a side length of 7 centimeters, as shown.
Note: Figure is not drawn to scale.
What is the area of the shaded region of the figure?
A.
4 square centimeters
B.
24 square centimeters
C.
12 square centimeters
D.
49 square centimeters
A square with a side length of 5 centimeters is cut out of a square with a side length of 7 centimeters, as shown.
Note: Figure is not drawn to scale.
What is the area of the shaded region of the figure?
A.
4 square centimeters
B.
24 square centimeters
C.
12 square centimeters
D.
49 square centimeters
Answers
GPT-4o mini
To find the area of the shaded region, we first need to calculate the area of both squares and then subtract the area of the smaller square from the area of the larger square.
1. **Calculate the area of the larger square** (side length = 7 cm):
\[
\text{Area}_{\text{large}} = \text{side}^2 = 7^2 = 49 \text{ square centimeters}
\]
2. **Calculate the area of the smaller square** (side length = 5 cm):
\[
\text{Area}_{\text{small}} = \text{side}^2 = 5^2 = 25 \text{ square centimeters}
\]
3. **Calculate the area of the shaded region**:
\[
\text{Area}_{\text{shaded}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} = 49 - 25 = 24 \text{ square centimeters}
\]
Thus, the area of the shaded region is **24 square centimeters**, which corresponds to option **B**.
1. **Calculate the area of the larger square** (side length = 7 cm):
\[
\text{Area}_{\text{large}} = \text{side}^2 = 7^2 = 49 \text{ square centimeters}
\]
2. **Calculate the area of the smaller square** (side length = 5 cm):
\[
\text{Area}_{\text{small}} = \text{side}^2 = 5^2 = 25 \text{ square centimeters}
\]
3. **Calculate the area of the shaded region**:
\[
\text{Area}_{\text{shaded}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}} = 49 - 25 = 24 \text{ square centimeters}
\]
Thus, the area of the shaded region is **24 square centimeters**, which corresponds to option **B**.