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The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2. Find: Surface area of the pyramid

Respuesta :

calculista

Answer:

The surface area of the pyramid is [tex]228\ cm^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of the Pyramid is equal to

[tex]SA=B+LA[/tex]

where

B is the area of the base of the pyramid

LA is the lateral area of the pyramid

In this problem we have

[tex]B=36\ cm^{2}[/tex]

Find the lateral area LA

Remember that the lateral area is the area of its four lateral faces

so

Multiply the area of a lateral face by 4 (because is a regular quadrilateral)

[tex]LA=(4)(48)=192\ cm^{2}[/tex]

Find the surface area SA

substitute the values

[tex]SA=36+192=228\ cm^{2}[/tex]

The surface area of the pyramid is 228 square cm.

What is the regular quadrilateral pyramid?

A pyramid is a three-dimensional shape. A pyramid has a polygonal base and flat triangular faces, which join at a common point called the apex.

The area of the base of the regular quadrilateral pyramid is 36 cm2 and the area of a lateral face is 48 cm2.

The surface area of the pyramid is;

[tex]\rm Surface \ area=B + LA[/tex]

Where; B is the area of the base of the pyramid, LA is the lateral area of the pyramid.

The area of a lateral face by 4 (because is a regular quadrilateral) is;

[tex]\rm LA=4(48)=192[/tex]

Substitute all the values in the formula;

[tex]\rm Surface \ area=B + LA\\\\\rm Surface \ area=36+192\\\\\rm Surface \ area=228[/tex]

Hence, the surface area of the pyramid is 228 square cm.

To know more about pyramids click the link given below.

https://brainly.com/question/11178083

#SPJ3

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