Question
This jewelry box is in the shape of a prism. One way you can find the surface area is by adding the area of the 2 bases, and the area of the long rectangle along the edges of the bases. Start by finding the area of the base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is
Answers
GPT-4o mini
To find the area of the base of a right triangular prism, we need to calculate the area of the triangular base first.
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of the triangular base measures 6 inches and its height measures 8 inches.
Substituting in the values:
\[
\text{Area} = \frac{1}{2} \times 6 \, \text{in} \times 8 \, \text{in}
\]
\[
\text{Area} = \frac{1}{2} \times 48 \, \text{in}^2
\]
\[
\text{Area} = 24 \, \text{in}^2
\]
Thus, the area of one base is \( 24 \, \text{in}^2 \).
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
In this case, the base of the triangular base measures 6 inches and its height measures 8 inches.
Substituting in the values:
\[
\text{Area} = \frac{1}{2} \times 6 \, \text{in} \times 8 \, \text{in}
\]
\[
\text{Area} = \frac{1}{2} \times 48 \, \text{in}^2
\]
\[
\text{Area} = 24 \, \text{in}^2
\]
Thus, the area of one base is \( 24 \, \text{in}^2 \).