Question

shape is a triangular prism with h=9 in, b=17 in, s1= 10 in, s2= 12, s3= 17 and l=10
SA =?

Answer 1

no

Answer 2

To find the surface area of a triangular prism, we need to calculate the areas of each face and then sum them up.

1. Calculate the area of the triangular bases:
The area of a triangle is given by the formula: 1/2 * base * height
The base of the triangle is given by side s3 = 17 in and the height is given by l = 10 in
Area of the triangular base = 1/2 * 17 * 10 = 85 square inches

2. Calculate the area of the three rectangular sides:
The area of a rectangle is given by the formula: length * width
The first rectangular side:
Length = l = 10 in, Width = s1 = 10 in
Area of the first side = 10 * 10 = 100 square inches

The second rectangular side:
Length = l = 10 in, Width = s2 = 12 in
Area of the second side = 10 * 12 = 120 square inches

The third rectangular side:
Length = h = 9 in, Width = b = 17 in
Area of the third side = 9 * 17 = 153 square inches

3. Finally, sum up all the areas to get the total surface area of the triangular prism:
SA = 2 * Area of triangular base + 3 * Area of rectangular sides
SA = 2 * 85 + 3 * (100 + 120 + 153)
SA = 170 + 3 * 373
SA = 170 + 1119
SA = 1289 square inches

Therefore, the surface area of the triangular prism is 1289 square inches.

Answer 3

I apologize for the mistake in my previous calculation. Let's recalculate the surface area of the triangular prism again.

1. Calculate the area of the triangular bases:
The area of a triangle is given by the formula: 1/2 * base * height
The base of the triangle is given by side s3 = 17 in and the height is given by l = 10 in
Area of each triangular base = 1/2 * 17 * 10 = 85 square inches
Since there are two triangular bases, the total area of the triangular bases = 2 * 85 = 170 square inches

2. Calculate the area of the three rectangular sides:
The area of a rectangle is given by the formula: length * width
Calculate the areas of the three rectangular sides:
First side: 10 * 10 = 100 square inches
Second side: 10 * 12 = 120 square inches
Third side: 9 * 17 = 153 square inches

3. Add up the areas of the triangular bases and the rectangular sides to find the total surface area of the prism:
SA = Total area of triangular bases + Total area of rectangular sides
SA = 170 + 100 + 120 + 153
SA = 543 square inches

Therefore, the surface area of the triangular prism with the given dimensions is 543 square inches.