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 one base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 in.
The area of one base is
in2. Decompose into rectangles, then add the area of each rectangle.
Right trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 in.
The area of one base is
in2. Decompose into rectangles, then add the area of each rectangle.
Answers
GPT-4o mini
To find the area of the base of the right trapezoidal prism, we first need to understand the shape of the base, which is a right trapezoid.
A right trapezoid has two parallel sides (the bases), which we usually refer to as the longer base (b1) and the shorter base (b2), and two heights.
In your case, you have the following dimensions:
- One base (b1) = 10 in (the longer base)
- The other base (b2) = 4 in (the shorter base)
- Height (h) = 6 in (the height between the two bases)
The area \( A \) of a trapezoid can be calculated using the formula:
\[
A = \frac{1}{2} (b1 + b2) \times h
\]
Substituting the values:
\[
A = \frac{1}{2} (10 + 4) \times 6
\]
\[
A = \frac{1}{2} (14) \times 6
\]
\[
A = 7 \times 6
\]
\[
A = 42 \text{ in}^2
\]
So, the area of one base of the prism is **42 in²**.
If you need to further decompose this trapezoid into rectangles to visualize or calculate each area, you could divide it as follows:
1. The larger rectangle formed by the longer base and height:
- Width = 10 in, Height = 6 in → Area = 10 * 6 = 60 in²
2. The smaller rectangle formed by the shorter base and the height:
- Width = 4 in, Height = 6 in → Area = 4 * 6 = 24 in²
3. The triangular part, which can be viewed as taking away the area of the smaller rectangle from the larger rectangle, or alternatively calculating the area of the triangle formed by the difference in height:
- Base = (10 in - 4 in) = 6 in,
- Height = (6 in) from the top of the shorter side to the longer top side.
- Area of triangle = \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 6 \times 6 = 18 \text{ in}^2\).
However, since the area of the trapezoid gives a direct answer, the simplest method without decomposition here is still \( 42 \text{ in}^2 \) for one base.
You can record this answer on Zearn.
A right trapezoid has two parallel sides (the bases), which we usually refer to as the longer base (b1) and the shorter base (b2), and two heights.
In your case, you have the following dimensions:
- One base (b1) = 10 in (the longer base)
- The other base (b2) = 4 in (the shorter base)
- Height (h) = 6 in (the height between the two bases)
The area \( A \) of a trapezoid can be calculated using the formula:
\[
A = \frac{1}{2} (b1 + b2) \times h
\]
Substituting the values:
\[
A = \frac{1}{2} (10 + 4) \times 6
\]
\[
A = \frac{1}{2} (14) \times 6
\]
\[
A = 7 \times 6
\]
\[
A = 42 \text{ in}^2
\]
So, the area of one base of the prism is **42 in²**.
If you need to further decompose this trapezoid into rectangles to visualize or calculate each area, you could divide it as follows:
1. The larger rectangle formed by the longer base and height:
- Width = 10 in, Height = 6 in → Area = 10 * 6 = 60 in²
2. The smaller rectangle formed by the shorter base and the height:
- Width = 4 in, Height = 6 in → Area = 4 * 6 = 24 in²
3. The triangular part, which can be viewed as taking away the area of the smaller rectangle from the larger rectangle, or alternatively calculating the area of the triangle formed by the difference in height:
- Base = (10 in - 4 in) = 6 in,
- Height = (6 in) from the top of the shorter side to the longer top side.
- Area of triangle = \(\frac{1}{2} \times base \times height = \frac{1}{2} \times 6 \times 6 = 18 \text{ in}^2\).
However, since the area of the trapezoid gives a direct answer, the simplest method without decomposition here is still \( 42 \text{ in}^2 \) for one base.
You can record this answer on Zearn.