Answer:
432in²
Step-by-step explanation:
Volume of a triangular based prism = [tex]Base\ area * height[/tex]
Base area = Area of the triangle = 1/2 * base of the triangle * height of the triangle
Since the triangular base has dimensions of 3" by 4" by 5", then it is a right angled triangle with base of 4in and height of 3in
Base Area = 1/2 * 3 * 4
Base Area = 6in²
Substituting the volume and the base area value in the formula to get the height of the prism we have;
210 = 6H
H = 210/6
H = 35in
Surface area of the triangular prism = bh + pH
b= base of the triangle = 4in
h- height of the triangle = 3in
p= perimeter of the triangle = 3+4+5 = 12in
H= height of the prism = 35in
Surface area of the triangular prism = 4(3)+12(35)
Surface area of the triangular prism = 12+420in
Surface area of the triangular prism = 432in²
