Answer:
surface area = 987 in²
Step-by-step explanation:
The surface of the right triangular prism has 5 surfaces , that is
• 2 congruent triangular faces
• rectangular base
• rectangular back
• rectangular inclined face
We require to calculate the area of these 5 surfaces and sum them
We require to calculate the length of QR in right Δ PQR
using Pythagoras' identity in right triangle PQR
a² + b² = c² ( c is the hypotenuse and a, b the legs )
here a = QR, b = PQ = MN = 14 , c = PR = 17.5 , then
QR² + 14² = 17.5²
QR² + 196 = 306.25 ( subtract 196 from both sides )
QR² = 110.25 ( take square root of both sides )
QR = [tex]\sqrt{110.5}[/tex] = 10.5 in
Then area of 2 congruent triangular ends is
A = 2 × [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
b = QR = 10.5 , h = PQ = 14 , then
A = bh = 10.5 × 14 = 147 in²
area of rectangular base = OR × QR = 20 × 10.5 = 210 in²
area of rectangular back = MN × NQ ( = OR) = 14 × 20 = 280 in²
area of rectangular inclined face = OR × PR = 20 × 17.5 = 350 in²
Then
total surface area = 147 + 210 + 280 + 350 = 987 in²
