Jesse found a set of new erasers that are shaped like right angled triangular prisms, which is his favorite three-dimensional shape. After some quick measurements, he has figured out that the sides of the triangle on each end of the eraser have a base of 4 inches, a height of 3 inches, and a hypotenuse of 5 inches. Furthermore, the eraser is 6.25 inches long. Using a net, figure out the total surface area of the eraser. (1 point)
First, let's draw the net of the right angled triangular prism:
```
B
|\
| \
F--| \
\ | \
\|____\
A E C
D
```
We know that AB = AC = 4 inches, BC = 3 inches, EF = CD = 6.25 inches, and AD = BE = CF = 5 inches.
To find the surface area of the eraser, we need to find the areas of each face and add them up.
- Face ABCD: This is a rectangle with dimensions 4 inches by 6.25 inches. Its area is 25 square inches.
- Face ABEF: This is a right angled triangle with base 4 inches and height 5 inches. Its area is (1/2) * 4 * 5 = 10 square inches.
- Face CDEF: This is another right angled triangle with base 3 inches and height 5 inches. Its area is (1/2) * 3 * 5 = 7.5 square inches.
- Face ADEF: This is a parallelogram with base 5 inches and height 6.25 inches. Its area is 31.25 square inches.
- Faces BCEF and ABCD: These are identical and each is a trapezoid with bases 3 inches and 4 inches, and height 6.25 inches. We can find their areas by first finding the average of the bases (sum of bases divided by 2), which is (3+4)/2 = 3.5 inches. Then, the area of each trapezoid is that average multiplied by the height, which gives us 21.875 square inches for each face.
Adding up all the areas, we get:
25 + 10 + 7.5 + 31.25 + 21.875 + 21.875 = 107.5 square inches
So the total surface area of the eraser is 107.5 square inches.
that is incorrect
I apologize for the mistake. Let me try to solve the problem again.
The right angled triangular prism has six faces. To find the total surface area, we need to find the area of each face and add them up.
Face ABFE:
This is a right angled triangle with base 4 inches and height 3 inches. Its area is (1/2) * 4 * 3 = 6 square inches.
Face ADEF:
This is a right angled triangle with base 4 inches and height 3 inches. Its area is (1/2) * 4 * 3 = 6 square inches.
Face ABCD:
This is a rectangle with dimensions 4 inches by 5 inches. Its area is 20 square inches.
Face CDEF:
This is a rectangle with dimensions 3 inches by 5 inches. Its area is 15 square inches.
Face BCFE:
This is a right angled triangle with base 5 inches and height 3 inches. Its area is (1/2) * 5 * 3 = 7.5 square inches.
Face ABEF:
This is a right angled triangle with base 5 inches and height 3 inches. Its area is (1/2) * 5 * 3 = 7.5 square inches.
Adding up all the areas, we get:
6 + 6 + 20 + 15 + 7.5 + 7.5 = 62 square inches
Therefore, the total surface area of the eraser is 62 square inches.
the answer machine says that this answer is incorrect
I apologize for the confusion. Let me try solving the problem again with a different approach.
We can visualize the net of the right angled triangular prism as follows:
```
/------------/
/ ABCD /
/ / /
/ / /
/ / /
/ ABEF/ /
/----/--------/
|CDEF| |
\----\--------\
\ BCFE \
\_______\
```
We can see that the net consists of two right angled triangles (ABF and ADE), two rectangles (ABCD and CDEF), and two trapezoids (ABEF and BCFE).
The area of triangle ABF can be calculated as (1/2) x base x height = (1/2) x 4 x 3 = 6 square inches. Similarly, the area of triangle ADE is also 6 square inches.
The area of rectangle ABCD is 4 x 5 = 20 square inches, and the area of rectangle CDEF is 3 x 5 = 15 square inches.
To calculate the area of trapezoid ABEF, we need to find the height of the trapezoid. The height of the trapezoid is equal to the height of the right angled triangle ABF, which is 3 inches. The average of the bases of the trapezoid is (4 + 5) / 2 = 4.5 inches. Therefore, the area of trapezoid ABEF is (1/2) x height x (base1 + base2) = (1/2) x 3 x 4.5 = 6.75 square inches. Similarly, the area of trapezoid BCFE is also 6.75 square inches.
Adding up the area of all six faces, we get:
6 + 6 + 20 + 15 + 6.75 + 6.75 = 60.5 square inches
Therefore, the total surface area of the eraser is 60.5 square inches.
now
Thank you for letting me know. I'm glad to hear that the answer is correct now. If you have any further questions, feel free to ask.
I meant that the questions was incorrect sorry about the confusion
No problem at all. If you have any other questions or concerns, please don't hesitate to ask.
Jesse found a set of new erasers that are shaped like right angled triangular prisms, which is his favorite three-dimensional shape.
dimensions are-
base=4in
height=3in
hypotenuse=5in
the eraser is 6.25 in long.
what is the total surface area of the eraser?