Use the image to answer the question.
An illustration shows a triangular prism with length 7 feet, width 4 feet, and perpendicular height of the triangular face 3 feet.
What is the total surface area of the two triangular bases of this tent?
(1 point)
12 square feet
that's right. can you show how you did it?
Sure! The total surface area of the two triangular bases can be found by using the formula for the area of a triangle, which is:
Area = (base x height) / 2
In this case, the triangular base has a base of 4 feet and a height of 3 feet (since it is perpendicular to the prism), so its area is:
Area = (4 x 3) / 2 = 6 square feet
Since there are two triangular bases, we can find the total area by multiplying the area of one by 2:
Total surface area of both triangular bases = 2 x 6 square feet = 12 square feet
oh ok
I'm glad I could help! Is there anything else you need assistance with?
Use the image to answer the question.
An illustration shows a triangular prism with length 6 inches, width 2 inches, perpendicular height of the triangular face 1.12 inches, and side of triangular face 1.5 inches.
What is the total surface area of this eraser? Your answer should have two decimal places
To find the total surface area of the eraser, we need to find the area of each face and then add them up. Since a triangular prism has two triangular faces and three rectangular faces, we will need to calculate the area of five faces in total.
First, let's find the area of one of the triangular faces. We can use the formula for the area of a triangle, which is:
Area = (base x height) / 2
In this case, the base of the triangle is 1.5 inches and the height (which is the perpendicular height of the triangular face) is 1.12 inches:
Area of one triangular face = (1.5 x 1.12) / 2 = 0.84 square inches
Since there are two triangular faces, the total area of both is:
Total area of both triangular faces = 2 x 0.84 square inches = 1.68 square inches
Next, let's find the area of the three rectangular faces. The area of a rectangle can be found using the formula:
Area = length x width
There are two rectangular faces with dimensions 6 inches by 2 inches:
Area of first rectangular face = 6 x 2 = 12 square inches
Area of second rectangular face = 6 x 2 = 12 square inches
There is one rectangular face with dimensions 1.5 inches by 2 inches:
Area of third rectangular face = 1.5 x 2 = 3 square inches
Now, we can find the total surface area by adding up the area of all five faces:
Total surface area = 1.68 + 12 + 12 + 3 = 28.68 square inches
Therefore, the total surface area of the eraser is 28.68 square inches (rounded to two decimal places).
not quite..
I apologize for the mistake. I think I misread the dimensions in the original question. Let me try again:
To find the total surface area of the eraser, we need to find the area of each face and then add them up. Since a triangular prism has two triangular faces and three rectangular faces, we will need to calculate the area of five faces in total.
First, let's find the area of one of the triangular faces. We can use the formula for the area of a triangle, which is:
Area = (base x height) / 2
In this case, the base of the triangle is 1.5 inches and the height (which is the perpendicular height of the triangular face) is 1.12 inches:
Area of one triangular face = (1.5 x 1.12) / 2 = 0.84 square inches
Since there are two triangular faces, the total area of both is:
Total area of both triangular faces = 2 x 0.84 square inches = 1.68 square inches
Next, let's find the area of the three rectangular faces. The area of a rectangle can be found using the formula:
Area = length x width
There are two rectangular faces with dimensions 6 inches by 1.5 inches:
Area of first rectangular face = 6 x 1.5 = 9 square inches
Area of second rectangular face = 6 x 1.5 = 9 square inches
There is one rectangular face with dimensions 2 inches by 1.12 inches:
Area of third rectangular face = 2 x 1.12 = 2.24 square inches
Now, we can find the total surface area by adding up the area of all five faces:
Total surface area = 1.68 + 9 + 9 + 2.24 = 21.92 square inches
Therefore, the total surface area of the eraser is 21.92 square inches (rounded to two decimal places).