SOLUTION: V-QRST is a rectangular pyramid with edge VS, base QRST. QR = 3/8 m, RS = 5/8 m, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answer

Algebra ->  Polygons -> SOLUTION: V-QRST is a rectangular pyramid with edge VS, base QRST. QR = 3/8 m, RS = 5/8 m, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answer       Log On


   

Question 1198369: V-QRST is a rectangular pyramid with edge VS, base QRST. QR = 3/8 m, RS = 5/8 m, and VS = 2/3 m. How many square centimeters are there on its lateral surface? Round off the answer to the nearest integer.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a=RS+=+%285%2F8%29m=62.5cm+
b=QR+=+%283%2F8%29m=+37.5cm+
VS+=+%282%2F3%29m=66.67cm+


to find the height of pyramid, first find the diagonal of the base
d%5E2=a%5E2%2Bb%5E2
d%5E2=+%2862.5cm%29%5E2%2B%2837.5cm%29%5E2
d%5E2=+5310cm%5E2
d+=+sqrt%285310cm%5E2%29
d+=+72.87cm

then
d%2F2+=%2872.87cm%29%2F2
d%2F2+=36.435cm

and, height is
h%5E2=%2866.67cm%29%5E2-%2836.435cm%29%5E2+
h%5E2=3117cm%5E2
h=sqrt%283117cm%5E2%29
h=55.8cm


The formula for calculating the surface area of the pyramid is:

SA=ab%2Ba%2Asqrt%28+%28b%2F2%29%5E2+%2Bh%5E2%29%2Bb%2Asqrt%28%28a%2F2%29%5E2+%2Bh%5E2%29


SA=2344cm%5E2+%2B3679cm%5E2+%2B2398cm%5E2
SA=8421cm%5E2+

answer: total surface area is 8421cm%5E2