Question

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.

Answer 1

Answer:

The lateral surface area is 755 sq.m. and total surface area is 785 sq.m.

Step-by-step explanation:

Let a, b, and c be the sides of the base and h be the height of the prism.

a = 5 m

b=6 m

c=11.21 m

h = 34 m

Lateral surface area of triangular prism = $(a+b+c)h$

                                                                 = $(5+6+11.21)34$

                                                                 =755.14 sq.m.

Total surface are of triangular prism = Lateral surface area + area of 2 triangles

                                                         =$755.14+2 (\frac{1}{2} \times b\times h)$

                                                         =$755.14+2 (\frac{1}{2} \times 5\times 6)$

                                                         =$785.14$

Thus the lateral surface area is 755 sq.m. and total surface area is 785 sq.m.

Option B is correct.

Answer 2

Answer:

The answer is A. 755 m2; 815 m2

Step-by-step explanation:

The answer is A) 472m^2; 486 m^2.

Let a, b, and c be the sides of the base and h be the height of the prism

a = 2 m

b = 7 m

c = 7.28 m

h = 29 m

The lateral surface area is:

LA = a*h + b*h + c*h = h * (a + b + c)

LA = 29 * (2 + 7 + 7.28) = 29 * 16.28 ≈ 472 m²

The surface area is:

SA = LA + 2 * 1/2 * a * b

SA = 472 + 2 * 7 = 472 + 14 = 486 m²