Triangular prism surface area 15 yd 8yd 15yd
A triangular prism has a base with three sides, and also a length.
You have only listed three numbers.
In any case, I assume you can find the area of a triangle and a rectangle.
The prism's surface comprises 2 triangles and three rectangles.
So add up all those areas.
If the base is an isosceles triangle with base=15 and altitude 8, then the two congruent sides are 17. So the area would be
2(8*15/2) + 17*15 + 17*15 + 8*15
To find the surface area of a triangular prism, you need to calculate the areas of the individual faces and add them together.
First, let's identify the faces of the triangular prism:
1. Triangular bases: There are two identical triangular faces at the top and bottom of the prism.
2. Rectangular sides: There are three rectangular faces that connect the corresponding edges of the triangular bases.
To calculate the surface area, we will compute the areas of each face and sum them up.
1. Triangular bases:
The formula for the area of a triangle is 1/2 * base * height.
In this case, the base and height of the triangular face are 15 yards and 8 yards respectively.
Area of one triangular base = 1/2 * 15 yd * 8 yd = 60 yd²
Since there are two identical bases, we multiply this value by 2.
Total area of the triangular bases = 2 * 60 yd² = 120 yd²
2. Rectangular sides:
To calculate the area of a rectangle, you multiply the length and width of the rectangle.
Here, two sides have dimensions 15 yards (length) and 8 yards (height), and the other side has dimensions 15 yards (length) and the height of the triangular base (8 yards).
Area of the first rectangular side = 15 yd * 8 yd = 120 yd²
Area of the second rectangular side = 15 yd * 8 yd = 120 yd²
Area of the third rectangular side = 15 yd * 15 yd = 225 yd²
Total area of the rectangular sides = 120 yd² + 120 yd² + 225 yd² = 465 yd²
Finally, to find the total surface area, we add the areas of the triangular bases and the rectangular sides:
Total surface area = Total area of the triangular bases + Total area of the rectangular sides
= 120 yd² + 465 yd²
= 585 yd²
Therefore, the surface area of the given triangular prism with dimensions 15 yd, 8 yd, and 15 yd is 585 square yards.