MATH SOLVE

2 months ago

Q:
# 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^2d. 100√6 cm^2e. 198√6 cm^2

Accepted Solution

A:

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

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