Answer:
The surface area of the triangular prism is 1554 square units
Explanation:
To find the surface area of a triangular prism, we need to add up the areas of all its faces. A triangular prism has two congruent triangular bases and three rectangular faces.
First, let's calculate the area of each triangular base. We can use the formula for the area of a triangle, which is A = 1/2 * base * height.
The base of each triangle is one of the sides of the triangle, and the height is the height of the prism, which is h = 21 units. We have:
Area of one triangular base = 1/2 * b * h = 1/2 * 29 * 21 = 304.5 square units
Since there are two congruent triangular bases, the total area of the bases is:
Total area of the bases = 2 * 304.5 = 609 square units
Next, let's calculate the area of each rectangular face. We can use the formula for the area of a rectangle, which is A = length * width.
The length of each rectangular face is one of the sides of the triangle, and the width is the height of the prism, which is h = 21 units. We have:
Area of one rectangular face = w * h = 15 * 21 = 315 square units
Since there are three rectangular faces, the total area of the rectangular faces is:
Total area of the rectangular faces = 3 * 315 = 945 square units
Finally, we can add up the areas of the bases and the rectangular faces to find the total surface area of the prism:
Total surface area = Total area of the bases + Total area of the rectangular faces
= 609 + 945
= 1554 square units
Therefore, the surface area of the triangular prism is 1554 square units.