MATHEMATICS HIGH SCHOOL

Pyramid ABCDE is a square pyramid.

What is the lateral area of pyramid ABCDE ?
Pyramid ABCDE is a square pyramid. What is the lateral - 1

Answers

Answer 1
Answer:

Answer:

A. 256√(3)\text{ in}^2

Step-by-step explanation:

Please find the attachment.

We have been given an image of a square pyramid ABCDE. We are asked to find the lateral area of pyramid.

First of all we need to find the height of pyramid.

The lateral height of the pyramid will be the length of altitude drawn from the lateral face of pyramid to the base of pyramid.

Since the base of pyramid is square, so the length of segment CM will be half the length of BC that is 16.

Since tangent relates the opposite and adjacent sides of a right triangle, so we can find the lateral height as:

\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}

\text{tan}(60^(\circ))=(AM)/(8)

√(3)=(AM)/(8)

√(3)* 8=(AM)/(8)* 8

8√(3)=AM

\text{Lateral surface area of pyramid}=(1)/(2)*pl, where,

p = Perimeter of the base,

l = Lateral or slant height.

\text{Lateral surface area of pyramid}=(1)/(2)*4*16*8√(3)

\text{Lateral surface area of pyramid}=2*16*8√(3)

\text{Lateral surface area of pyramid}=256√(3)

Therefore, the lateral surface area of our given pyramid is 256√(3) square inches and option A is the correct choice.
Answer 2
Answer:

Answer:

256√3 in^2.

Step-by-step explanation:

tan 60 = lateral height of 1 face / 8

Lateral height = 8 tan 60 = 8√3

Area of 1 face = 8 * 8√3 = 64√3

Lateral Area = 4 * 64√3 = 256√3 in^2

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Answers

Answer:

48. x 2

Step-by-step explanation:

4.8 x 2

An item regularly priced at $80 is on sale for 20% off. There is a 3% sales tax. What is the sale price before sales tax?

Answers

Answer:

The answer is $64.

Step-by-step explanation:

An item regularly priced at $80 is on sale for 20% off.

This amount becomes:

0.20*80=16 dollars

So, price after discount is 80-16=64 dollars

Given is that there is a 3% sales tax.

So, sales tax must have been applied to $64 before final bill.

And we have to tell the sale price before tax, so the answer is $64.

Therefore, the answer is $64.
the sale price before the sale tax is $ 60 and the sales taxes will be $ 180

Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?

Answers

assuming that the river doesn not move
if they kept a constand speed then they passes
the problem doesn't say how fast they were moving, but we can see that 1 boat is faster so

first pass
1400 meters from 1 bank
if they turn around they are 600 meters from the other bank
since they kept constant speed, they passed in the same place so
distance from bank1 to markx=1400
distance from bank2 to markx=600
distance from bank1 to bank2=600+1400
1400+600=total distance=2000 m

A catering service offers appetizers, main courses, and desserts. A banquet chairperson is to select appetizers, main courses, and desserts for a banquet. In how many ways can this be done?

Answers

(Number of appetizers) x (number of main courses) x (number of desserts)

Jacob trims trees and mows lawns during the summer months he earns 50$ per lawn and 120$ per tree he wants to purchase a car for 4,500if Jacob plans to mow 45 lawns this summer how many trees must he trim to earn at least 4,500

Answers

Answer:

  at least 19

Step-by-step explanation:

Let t represent the number of trees Jacob needs to trim. He wants ...

  50(45) +120t ≥ 4500

  120t ≥ 2250 . . . . . . . . . subtract 2250

  t ≥ 18.75

Jacob must trim at least 19 trees to earn at least $4500.

the measures of two angles of a triangle are 35 degrees and 45 degrees. what is the measure of the third angle of the triangle?

Answers

If it is a triangle, the total degree should be equal to 180.
So the last angle
180 - (35+45)
180 - 80
100
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