The figure below is a net for a triangular prism. Side a = 23 feet, side b = 14 feet, side c = 13 feet, side d = 13 feet, and side e = 19 feet. What is the surface area of this figure?
First, we need to identify the different faces of the prism. From the net, we can see that there are three rectangular faces (ABFE, BCGF, and CDHG), and two triangular faces (ABD and EFC).
To find the surface area, we need to calculate the area of each face and then add them up. Let's start with the rectangular faces:
- ABFE: This face has dimensions 23 by 14, so its area is 23 x 14 = 322 square feet.
- BCGF: This face is identical to ABFE, so it also has an area of 322 square feet.
- CDHG: This face has dimensions 19 by 14, so its area is 19 x 14 = 266 square feet.
Now let's move on to the triangular faces:
- ABD: This is a right triangle with legs of length 23 and 13, so its area is (1/2) x 23 x 13 = 149.5 square feet.
- EFC: This is also a right triangle, with legs of length 19 and 13. Its area is (1/2) x 19 x 13 = 123.5 square feet.
Finally, we can add up the areas to get the total surface area:
322 + 322 + 266 + 149.5 + 123.5 = 1183 square feet.
Therefore, the surface area of the triangular prism is 1183 square feet.
To find the surface area of the given triangular prism, we need to calculate the area of each face and then sum them up.
1. Start by identifying the faces of the triangular prism. It consists of two triangular bases and three rectangular lateral faces.
2. Calculate the area of the rectangular lateral faces:
- Lateral face 1 = side a x side e = 23 feet x 19 feet
- Lateral face 2 = side b x side e = 14 feet x 19 feet
- Lateral face 3 = side c x side e = 13 feet x 19 feet
3. Calculate the area of the triangular bases:
- Base 1 = 1/2 x base length x height = 1/2 x side a x side b
- Base 2 = 1/2 x base length x height = 1/2 x side c x side d
4. Add up all the face areas to find the surface area:
- Surface Area = 2 x (Area of triangular base) + 3 x (Area of rectangular lateral face)
Plug in the given values and perform the calculations to find the surface area of the figure.