Question

practice
a triangular prism has equilateral triangular
bases with bases 6 feet long and 5.2 feet tall.
the triangular prism has a height of 15 feet.
what is the total surface area?
a. 139.2 ft²
b. 265.2 ft²
c. 270 ft²
d. 301.2 ft²

Explanation:

Step1: Calculate area of two triangular bases

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. For each equilateral triangular base, base = 6 ft, height = 5.2 ft. So area of one triangle is $\frac{1}{2} \times 6 \times 5.2 = 15.6$ $ft^2$. Two triangles: $2 \times 15.6 = 31.2$ $ft^2$.

Step2: Calculate lateral surface area

The lateral surface area of a prism is perimeter of base $\times$ height of prism. Perimeter of equilateral triangle base: $3 \times 6 = 18$ ft. Height of prism is 15 ft. So lateral surface area: $18 \times 15 = 270$ $ft^2$. Wait, no, wait, maybe I messed up. Wait, the triangular prism's lateral faces: each is a rectangle with length 6 ft and height 15 ft? Wait, no, the height of the prism is 15 ft, and the base sides are 6 ft. Wait, but the triangular base has sides 6 ft (equilateral), so each lateral face is a rectangle with dimensions 6 ft (base side) and 15 ft (prism height). So three lateral faces: $3 \times (6 \times 15) = 270$? But then total surface area is lateral + 2 bases: $270 + 31.2 = 301.2$? Wait, no, wait the problem says "height of 5.2 feet" for the triangle? Wait, the problem says: "equilateral triangular bases with bases 6 feet long and 5.2 feet tall". Wait, maybe the triangle's height is 5.2 ft, and the prism's height (length) is 15 ft. So area of one triangle: $\frac{1}{2} \times 6 \times 5.2 = 15.6$, two triangles: 31.2. Then lateral surface area: perimeter of triangle (36=18) times prism height (15): 1815=270. Then total surface area: 270 + 31.2 = 301.2. So option D. Wait, but let's check again. Wait, maybe the diagram shows something else. Wait, the diagram has 6 ft as the base of the triangle, 5.2 ft as the height of the triangle, and 15 ft as the length of the prism. So yes, total surface area = 2(area of triangle) + perimeter of triangle length of prism. So 2(0.565.2) + 3615 = (65.2) + 270 = 31.2 + 270 = 301.2. So answer D.

Answer:

D. 301.2 $ft^2$