MATH SOLVE

2 months ago

Q:
# The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of one of the lateral faces is 105 cm2. Find:

Accepted Solution

A:

the complete question in the attached figure

we know that

A regular quadrilateral is a shape that has four equal sides, with all the interior angles equal

so

is a square

[perimeter of a square]=4*a

a-----> the length side of a square

60=4*a------> a=60/1-----> a=15 cm

Part A)

[surface area]=2*[area of the base]+4*[area of one lateral face]

area of the base=a²-----> 15²---> 225 cm²

area of one lateral face=105 cm²

[surface area]=2*[225]+4*[105]------> 450+420-----> 870 cm²

the answer Part A) is

surface area is 870 cm²

Part B)

[volume of the prism]=area of the base*height

height of the prism=area of one lateral face/length side of the base

height of the prism=105/15-------> 7 cm

[volume of the prism]=225*7-------> 1575 cm³

the answer Part B) is

the volume of the prism is 1575 cm³

we know that

A regular quadrilateral is a shape that has four equal sides, with all the interior angles equal

so

is a square

[perimeter of a square]=4*a

a-----> the length side of a square

60=4*a------> a=60/1-----> a=15 cm

Part A)

[surface area]=2*[area of the base]+4*[area of one lateral face]

area of the base=a²-----> 15²---> 225 cm²

area of one lateral face=105 cm²

[surface area]=2*[225]+4*[105]------> 450+420-----> 870 cm²

the answer Part A) is

surface area is 870 cm²

Part B)

[volume of the prism]=area of the base*height

height of the prism=area of one lateral face/length side of the base

height of the prism=105/15-------> 7 cm

[volume of the prism]=225*7-------> 1575 cm³

the answer Part B) is

the volume of the prism is 1575 cm³