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Lyrx [107]
3 years ago
11

What is the slant height of a regular pyramid if its lateral area is 160 units² and the perimeter of the base is 40 units?

Mathematics
2 answers:
SSSSS [86.1K]3 years ago
6 0

Answer:

The slant height of a regular pyramid is l=8\ units

Step-by-step explanation:

we know that

The lateral area of a regular pyramid is equal to

LA=\frac{1}{2}Pl

where

LA is the lateral area

P is the perimeter of the base

l is the slant height

we have

LA=160\ units^{2}

P=40\ units

substitute in the formula and solve for l

160=\frac{1}{2}(40)l

160=20l

l=160/20

l=8\ units

Gelneren [198K]3 years ago
5 0

The slant Height of a regular Pyramid with a lateral area of 160 units² and a perimeter of the base of 40 units is 8 units.

<h2>Further Explanation; </h2><h3>Regular Pyramid</h3>
  • A regular Pyramid is a pyramid whose base is a regular polygon and has equal lateral edges.
  • Therefore, lateral faces of a regular pyramid are congruent isosceles triangle.
  • Slant height of the regular pyramid is equivalent to the altitude of the lateral isosceles triangles.
<h3>Lateral Area of a regular Pyramid</h3>
  • The Lateral Area of a regular pyramid is given by the equation.

LA=\frac{1}{2}Pl

Where LA is the lateral area, P is the base perimeter and l is the slant height

In our question;

We are given;

Lateral area = 160 units²

Base perimeter = 40 units

We can use the formula to get the slant height, l.

Substituting the value of LA and P in the formula

160= \frac{1}{2}940)l\\160 = 20 l\\l = 160/20\\l = 8 units

Therefore the slant height of the regular Pyramid is 8 units.

Keywords: Regular pyramid, lateral area, base perimeter, slant height.

<h3>Learn more about:</h3>
  • Regular Pyramid:brainly.com/question/10081142
  • Lateral area of a regular pyramid: brainly.com/question/10081142
  • Example: brainly.com/question/10081142

Level: High school

Subject: Mathematics

Topic: Surface Area of solids

Sub-topic: Surface area of regular Pyramid

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