Use formulas to find the lateral area and surface area of the prism.

23 in.
15 in.
12 in.
Question content area bottom
Part 1
The lateral area of the prism is
A.
L.A.​ = 1,242 insquared and S.A.​ = 2,178 insquared
B.
L.A.​ = 828 insquared and S.A.​ = 882 insquared
C.
L.A.​ = 828 insquared and S.A.​ = 936 insquared
D.
L.A.​ = 59 insquared and S.A.​ = 177 insquared

1 answer

To find the lateral area of the prism, we can use the formula:

Lateral Area = 2h(l1 + l2 + l3)

where h is the height of the prism, and l1, l2, l3 are the three side lengths of the prism.

Given:
h = 23 in.
l1 = 15 in.
l2 = 12 in.

Plugging in the values:

Lateral Area = 2(23)(15 + 12 + 15)
Lateral Area = 2(23)(42)
Lateral Area = 2(966)
Lateral Area = 1,932 in²

Therefore, the lateral area of the prism is 1,932 in².

To find the surface area of the prism, we can use the formula:

Surface Area = 2(l1w1 + l2w2 + l3w3) + Lateral Area

where l1, w1, l2, w2, l3, w3 are the three side lengths and their corresponding widths.

Given:
w1 = w2 = w3 = 23 in.

Plugging in the values:

Surface Area = 2(15*23 + 12*23 + 15*23) + 1,932
Surface Area = 2(345 + 276 + 345) + 1,932
Surface Area = 2(966) + 1,932
Surface Area = 1,932 + 1,932
Surface Area = 3,864 in²

Therefore, the surface area of the prism is 3,864 in².

So, the correct answer is C. L.A.​ = 1,932 insquared and S.A.​ = 3,864 insquared.