Question

The base of a triangular prism is an isosceles right triangle with a hypotenuse of 72−−√ centimeters. The height of the prism is 7 centimeters. Find the surface area of the triangular prism. Round your answer to the nearest tenth.

Answer 1

Answer:

Step-by-step explanation:

Surface area = lateral area + 2(area of base)

Lateral area = perimeter of base * height.

Because it is a isosceles right triangle, both sides are equal.

$x^{2} +x^{2}$ = 72

2$x^{2}$ = 72. Divide both sides by 2

$x^{2}$ = 36.  Square both sides.

x = 6.

So the perimeter of the base = 6 + 6 +$\sqrt{72}$ = 20.485281374239

Lateral area = 20.485281374239 * 7 = 143.397 $cm^{2}$

Area of base is (1/2)base * height.

(1/2)(6)(6) = 18

Using the surface area formula

surface area = 143.397 + 2(18) = 179.4 $cm^{3}$