Question

1. Find the surface area of the right triangular prism below.

A. 264 in2

B. 246 in2

C. 408 in2

D. 384 in2

2. Find the value of p of the right triangular prism if the surface area is 120 in2.

A. 6 in

B. 8 in

C. 12 in

D. 9 in

Answer 1

2. D.
`\displaystyle 9\:in.`

1. C.
`\displaystyle 408\:in.^2`

Explanation:

`\displaystyle 2A_B + h[c + b + a] = S.A.`

Area of a Triangle [keep this in mind to find the base area]:

`\displaystyle (1)/(2)bh = A, (1)/(2)hb = A, or\:(hb)/(2) = A`

Pythagorean Theorem [You will need this theorem to find the lengths of both hypotenuses on both triangular bases]:

`\displaystyle a^2 + b^2 = c^2`

2.
`\displaystyle 2A_B + p[c + 3 + 4] = 120 → 2[6] + p[5 + 3 + 4] = 120 \\ \\ 12 + 12p = 120 → 108 = 12p; 9 = p`

1.
`\displaystyle 2A_B + 15[c + 6 + 8] = S.A. → 2[24] + 15[10 + 6 + 8] = S.A. \\ \\ 48 + 15[24] = S.A. → 48 + 360 = S.A.; 408 = S.A.`

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