Ask question

Ask question

All categories

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?

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

You might be interested in

If a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function?

pashok25 [27]

Answer: (an)(x)

Step-by-step explanation:

quizlet

8 0

3 years ago

Generate the nest three terms of each arithmetic sequence shown below.

o-na [289]

Answer:

A)2,6,10

B)2,-6,-18

C)-1,-3,-5

Step-by-step explanation:

<u>A)a1=-2 and d=4</u>

We know that the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{2}=a_{1}+(2-1)d$

$a_{2}=a_{1}+(1)d$

Substituting the given value we get

$a_{2}= -2+(1)4$

$a_{2}= -2+4$

$a_{2}= 2$

------------------------------------------

Similarly

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the given value we get

$a_{3}= -2+(2)4$

$a_{3}= -2+8$

$a_{3}= 6$

-------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the given value we get

$a_{4}= -2+(3)4$

$a_{4}= -2+16$

$a_{4}= 10$

-------------------------------------------------------------------------------------------

<u>B</u><u> $a_n=a_{(n-1)}-8$ with $a_1=10$ </u>

$a_2=a_{(2-1)}-8$

$a_2=a_{1}-8$

Substituting the given value

$a_2= 10-8$

$a_2=2$

---------------------------------------------------------------------

$a_3=a_{(3-1)}-8$

$a_3=a_{2}-8$

Substituting the value

$a_3=2-8$

$a_3= -6$

---------------------------------------------------------------------

$a_4=a_{(4-1)}-8$

$a_4=a_{3}-8$

Substituting the value

$a_4= -6-8$

$a_4= -14$

-------------------------------------------------------------------------------------------

<u>C) $a_1=3, a_2=1$ </u>

Here the difference is -2

the arithmetic sequence formula is

$a_{n}=a_{1}+(n-1)d$

Now

$a_{3}=a_{1}+(3-1)d$

$a_{3}=a_{1}+(2)d$

Substituting the value we get

$a_{3}= 3+(2)-2$

$a_{3}= 3-4$

$a_{3}= -1$

------------------------------------------------------------------------------

$a_{4}=a_{1}+(4-1)d$

$a_{4}=a_{1}+(3)d$

Substituting the value we get

$a_{4}= 3+(3)-2$

$a_{4}= 3-6$

$a_{4}= -3$

----------------------------------------------------------------------------------

$a_{5}=a_{1}+(5-1)d$

$a_{5}=a_{1}+(4)d$

Substituting the value we get

$a_{5}= 3+(4)-2$

$a_{5}= 3-8$

$a_{5}= -5$

4 0

3 years ago

You are making identical bagel platters using 40 plain bagels, 30 raisin bagels, and 24 blueberry bagels. what is the greatest n

Marat540 [252]

Answer:

100

Step-by-step explanation:

94 bagels in total. 100 will be plenty

4 0

3 years ago

Read 2 more answers

Find the missing length of the triangle. <br> 20 km <br> 21 km <br> WHAT IS “C” PLEASE HELP

Leno4ka [110]

Answer:

C=29

Step-by-step explanation:

a^2 + b^2 = c^2

21^2 + 20^2 = c^2

441 + 400 = c^2

841 = c^2

\sqrt(841) = \squrt(c^2)

29 = c

6 0

2 years ago

Read 2 more answers

Halp me please i need HALPPPPPPPPPP

Ira Lisetskai [31]

Answer:

I think the answer is 5000000

Step-by-step explanation:

8 0

3 years ago