What is the surface area of the box, in square meters, that Jeriel decorates, given the net of the right rectangular prism?
Understand the Problem
The question is asking to determine the surface area of a right rectangular prism given its net. To do this, we will calculate the area of each rectangle in the net and sum them together to get the total surface area.
Answer
$448 \text{ m}^2$
Answer for screen readers
$448 \text{ m}^2$
Steps to Solve
- Identify the rectangles and their dimensions
From the net of the rectangular prism, we can identify the dimensions of the rectangles. We have three pairs of congruent rectangles. Rectangle 1: 10 m x 7 m Rectangle 2: 15 m x 7 m Rectangle 3: 7 m x 7 m
- Calculate the area of each rectangle
To find the area of each rectangle, we multiply its length by its width. Area of Rectangle 1: $10 \text{ m} \times 7 \text{ m} = 70 \text{ m}^2$ Area of Rectangle 2: $15 \text{ m} \times 7 \text{ m} = 105 \text{ m}^2$ Area of Rectangle 3: $7 \text{ m} \times 7 \text{ m} = 49 \text{ m}^2$
- Calculate the total surface area
Since there are two of each rectangle, we multiply each individual area by 2 and add them together. Total Surface Area = $2 \times \text{Area of Rectangle 1} + 2 \times \text{Area of Rectangle 2} + 2 \times \text{Area of Rectangle 3}$ Total Surface Area = $2 \times 70 \text{ m}^2 + 2 \times 105 \text{ m}^2 + 2 \times 49 \text{ m}^2$ Total Surface Area = $140 \text{ m}^2 + 210 \text{ m}^2 + 98 \text{ m}^2$ Total Surface Area = $448 \text{ m}^2$
$448 \text{ m}^2$
More Information
The surface area is the total area of the faces of the 3-dimensional figure.
Tips
A common mistake is forgetting to multiply the area of each rectangle by 2, since there are two identical rectangles for each face of the prism. Also forgetting units is a common mistake, surface area is measured in units $\text{m}^{2}$.
AI-generated content may contain errors. Please verify critical information
