Respuesta :

calculista
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 

 

Ver imagen calculista

The surface area of a regular quadrilateral prism whose perimeter of the base is 60 cm, is 870 cm².

What is of total surface area of the regular prism?

The total surface area of the regular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of the prism.

Total surface area of the regular prism is calculated with the following formula.

[tex]A_{s}=2a^2+4A_l[/tex]

Here, (a) is the side of the base and (Al) is the lateral area of one side.

The perimeter of the base of a regular quadrilateral prism is 60 cm. The perimeter of the base of a regular quadrilateral prism is 4 times the length of it (say a). Thus,

[tex]4a=60\\a=\dfrac{60}{4}\\a=15\rm\; cm[/tex]

The area of one of the lateral faces is 105 cm2. Thus,

[tex]A_{s}=2(15)^2+4\times105\\A_s=450+420\\A_s=870\rm\; cm^2[/tex]

Hence, the surface area of a regular quadrilateral prism whose perimeter of the base is 60 cm, is 870 cm².

Learn more about the surface area of a prism here;

https://brainly.com/question/15456870

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