Unit six surface area lesson four surface area of triangular prisms quick check five questions and I’m on question four use the image to answer the question. The front base is 16 m² the right bottom length is 11 m. The left length is 17 m and the back bait is 17 m And on and on the other left side is another 15 m so what the surface area the triangular prism be eight22 m² or 768 m² or 77 9 m² are 790 m²
The correct answer is 768 m².
To find the surface area of a triangular prism, you need to calculate the area of the two triangular faces and the three rectangular faces, and then add them together.
The area of the two triangular faces can be calculated by using the formula A = 1/2 * base * height. In this case, the front base is 16 m² and the height can be calculated using the Pythagorean theorem, as it is a right-angled triangle.
Front base = 16 m²
Right bottom length = 11 m
Left length = 17 m
Back base = 17 m
Other left side = 15 m
Using Pythagorean theorem:
height = √(17^2 - 15^2)
height = √(289 - 225)
height = √64
height = 8 m
Now, calculate the area of the two triangular faces:
Front face area = 1/2 * 16 * 8 = 64 m²
Back face area = 1/2 * 17 * 8 = 68 m²
Next, calculate the area of the three rectangular faces:
Right face area = 16 * 11 = 176 m²
Left face area = 17 * 15 = 255 m²
Bottom face area = 17 * 11 = 187 m²
Finally, add all the areas together to find the total surface area of the triangular prism:
Total surface area = 64 + 68 + 176 + 255 + 187 = 750 m²
Therefore, the correct answer is 750 m².