triangular prism with base perimeter 24 cm, base area 24 cm^2, and height 15 cm.
Choices are:
A. 606 cm^2
B. 384 cm^2
C. 408 cm^2
D. 87 cm^2
24*15=360 lateral area
2*24 = 48 bases
(C)
To find the surface area of a triangular prism, we need to calculate the areas of the two triangular bases and the surface area of the three rectangular faces.
Let's start by finding the area of one triangular base. Since the base has a perimeter of 24 cm, it means that each side of the triangle has a length of 24 cm divided by 3, which is 8 cm. Using the formula for the area of a triangle A = (1/2) * base * height, we can calculate the area:
Area of triangular base = (1/2) * 8 cm * height of the triangle
= 4 cm * height of the triangle
Given that the base area is 24 cm^2, we can use the formula for the area of the triangle to solve for the height of the triangle:
24 cm^2 = 4 cm * height of the triangle
height of the triangle = 24 cm^2 / 4 cm
height of the triangle = 6 cm
Now, let's calculate the area of one triangular base using this height:
Area of triangular base = 4 cm * 6 cm
= 24 cm^2
Since there are two triangular bases, the total area of the triangular bases is:
Total area of triangular bases = 2 * Area of one triangular base
= 2 * 24 cm^2
= 48 cm^2
Next, let's find the surface area of the three rectangular faces. The base perimeter is 24 cm, which means that the length of each rectangular face is 8 cm. The height of the rectangular faces is given as 15 cm.
Since there are three rectangular faces, the total surface area of the three rectangular faces is:
Total surface area of rectangular faces = 3 * length * height
= 3 * 8 cm * 15 cm
= 360 cm^2
Finally, to find the total surface area of the triangular prism, we sum the areas of the triangular bases and the surface area of the rectangular faces:
Total surface area = Total area of triangular bases + Total surface area of rectangular faces
= 48 cm^2 + 360 cm^2
= 408 cm^2
Therefore, the correct choice is:
C. 408 cm^2