Use the image to answer the question.
The image is a rectangle with the following measurements and values:- Side lengths of 3m and 8m- A diagonal of 13m- A missing value of 2.6 ml- A missing value of 1It seems to be a diagram or plot with text and lines.
What is the surface area of the triangular prism shown as a net? Round the answer to the nearest tenth.
(1 point)
m2
The surface area of the triangular prism shown as a net can be calculated by finding the areas of each face of the prism and adding them together.
First, we calculate the area of the rectangle which is the base of the prism:
Area = length x width
Area = 3m x 8m
Area = 24m^2
Next, we calculate the area of the two triangles which are the sides of the prism. The two missing values indicate that these triangles are both isosceles triangles.
To find the height of the triangle (the segment perpendicular to the base from the tip of the triangle), we can use the Pythagorean theorem:
a^2 + b^2 = c^2
2.6^2 + h^2 = 13^2
6.76 + h^2 = 169
h^2 = 162.24
h ≈ 12.74m
Now, we can calculate the area of one of the triangles:
Area = 1/2 x base x height
Area = 1/2 x 3m x 12.74m
Area ≈ 19.11m^2
The total surface area of the triangular prism is:
24m^2 + 2(19.11m^2) = 62.22m^2
So, the surface area of the triangular prism shown as a net is approximately 62.2m^2.
stop getting random numbers pls
Apologies for the error in the previous response. Let's correct that and calculate the surface area of the triangular prism shown as a net using rounded numbers.
Given:
Side lengths of the rectangle: 3m and 8m
Diagonal of the rectangle: 13m
First, let's find the missing height of one of the isosceles triangles:
Using the Pythagorean theorem:
3^2 + h^2 = 13^2
9 + h^2 = 169
h^2 = 160
h ≈ 12.6m
Now, let's calculate the surface area of the triangular prism:
Base area = length x width = 3m x 8m = 24m^2
Triangle area = 1/2 x base x height = 1/2 x 3m x 12.6m = 18.9m^2
Total surface area = 2(triangle area) + rectangle area = 2(18.9m^2) + 24m^2 = 37.8m^2 + 24m^2 = 61.8m^2
Therefore, the surface area of the triangular prism shown as a net is approximately 61.8 square meters.