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2 years ago

How do you find surface area of a triangular prism ?

Mathematics

1 answer:

Vitek1552 [10]2 years ago

6 0

Answer:

See below.

Step-by-step explanation:

To find the surface area, find the area of the square base and add it to the area of each triangle face. Find the area of the base by multiplying base length by base length. Find the area of each triangle face by multiplying 1/2 * b*h.

Example:

For a base which is 12 by 12. The area is 12 x 12 = 144.

For the triangle face, the area is 1/2 * 12 * 15 = 90. Since there are 4 faces, the total area is 4 * 90 = 360.

Together the surface area is 360 + 144 = 504.

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The following picture is a square pyramid where DE=8 cm and m∠ADE=60°.

Goryan [66]

Given:

The length of DE is 8 cm and the measure of ∠ADE is 60°.

We need to determine the surface area of the pyramid.

Length of AD:

The length of AD is given by

$cos 60^{\circ}=\frac{FD}{8}$

$4=FD$

Length of AD = 8 cm

Slant height:

The slant height EF can be determined using the trigonometric ratio.

Thus, we have;

$sin \ 60^{\circ}=\frac{EF}{8}$

$sin \ 60^{\circ} \times 8=EF$

$\frac{\sqrt{3}}{2} \times 8=EF$

$4\sqrt{3}=EF$

Thus, the slant height EF is 4√3

Surface area of the square pyramid:

The surface area of the square pyramid can be determined using the formula,

$SA=Area \ of \ square + \frac{1}{2} (Perimeter \ of \ base ) (slant \ height)$

Substituting the values, we have;

$SA=8^2+\frac{1}{2}(8+8+8+8)(4 \sqrt{3})$

$SA=64+\frac{1}{2}(32)(4 \sqrt{3})$

$SA=64+(16)(4 \sqrt{3})$

$SA=64+64 \sqrt{3}$

The exact form of the area of the square pyramid is $64+64 \sqrt{3}$

Substituting √3 = 1.732 in the above expression, we have;

$SA = 64 + 110.848$

$SA = 174.848$

Rounding off to one decimal place, we get;

$SA = 174.8$

Thus, the area of the square pyramid is 174.8 cm²

7 0

2 years ago

Read 2 more answers

What happens to ice as it melts

Ludmilka [50]

It becomes a liquid
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3 0

3 years ago

Read 2 more answers

if a car travels 370.3 miles on 52 liters of gas, how many liters of.gas.will take to go 722 miles.if the car travels at the sam

blsea [12.9K]

Answer:

101.4 liters.

Step-by-step explanation:

First of all we will find mileage of car.

$\text{Mileage of car}=\frac{\text{Total distance traveled}}{\text{Total amount of fuel}}$

$\text{Mileage of car}=\frac{370.3\text{ miles}}{52\text{ liters gas}}$

$\text{Mileage of car}=7.12115\frac{\text{ miles}}{\text{ liters gas}}$

We can see that car travels at the rate of 7.12 miles per liter gas. Now let us find amount of gas needed to travel 722 miles at the same rate.

$\text{Amount of gas needed}=\frac{722}{7.12}$

$\text{Amount of gas needed}=101.388$

Therefore, it will take 101.4 liters of gas to travel 722 miles.

4 0

2 years ago

What was a effect on the war of 1812 PLEASE HURRY AND HELP ME

labwork [276]

Answer:

The War of 1812 changed the course of American history. Because America had managed to fight the world's greatest military power to a virtual standstill, it gained international respect. Furthermore, it instilled a greater sense of nationalism among its citizens.

Step-by-step explanation:

8 0

2 years ago

The value of homes sold in Hampton VA are normally distributed with a mean of $200,000 and a standard deviation of $10,000. If 1

LenKa [72]

Answer:

84%

Step-by-step explanation:

What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.

We have that z is equal to:

z = (x - m) / (sd)

x is the value to evaluate, m the mean, sd the standard deviation

So for 190000 we have:

z = (190000 - 200000) / (10000)

z = -1

and this value represents 0.1587

for 230000 we have:

z = (230000 - 200000) / (10000)

z = 3

and this value represents 0.9987

we subtract:

0.9987 - 0.1587 = 0.84

Which means that it represents 84% of the houses

3 0

2 years ago

How do you find surface area of a triangular prism ?​

How do you find surface area of a triangular prism ?