Question

Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm.
a. 92√6 cm^2 
b. 96√6 cm^2 
c. 180√6 cm^2
d. 100√6 cm^2
e. 198√6 cm^2

Answer 1

Let
x------> the larger side of the rectangular base
y-------> the smaller side of the rectangular base

we know that
Applying the Pythagoras theorem

for the larger side of the base
slant height =13 cm
h=5 cm
13²=5²+(x/2)²-----> (x/2)²=13²-5²-----> 144
(x/2)²=144------> x/2=12------> x=24 cm

for the smaller side of the base
slant height =7 cm
h=5 cm
7²=5²+(y/2)²-----> (y/2)²=7²-5²-----> 24
(y/2)²=24------> y/2=√24------> y=4√6 cm

the area of the base is
24*4√6------> 96√6 cm²

the answer is the option
b. 96√6 cm^2