Question

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?

Answer 1

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

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

$160=20l$

$l=160/20$

$l=8\ units$

Answer 2

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.

Further Explanation;

Regular Pyramid

• 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.

Lateral Area of a regular Pyramid

• 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.

Learn more about:

• 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