All categories

3 years ago

Find the total surface area of this prism where

Mathematics

1 answer:

bulgar [2K]3 years ago

8 0

Answer:

The total surface area of the prism is 620 cm²

Step-by-step explanation:

The total area of the prism = lateral area + 2 (area of the cross-section)

The lateral area = perimeter of the cross-section × height

∵ The cross-section of the prism is an isosceles triangle

∵ The sides of the triangle are 13 cm, 13 cm, 24 cm

∵ The perimeter of the triangle is the sum of its sides

∴ The perimeter = 13 + 13 + 24 = 50 cm

∴ The perimeter of the cross-section = 50 cm

∵ The height of the prism is 10 cm

→ Use the rule of the lateral area above to find it

∴ The lateral area of the prism = 50 × 10 = 500 cm²

∵ The area of the triangle = $\frac{1}{2}$ × base × height

∵ The base of the triangle = 24 cm

∵ The height of the triangle = 5 cm

∴ The area of the triangle = $\frac{1}{2}$ × 24 × 5 = 60 cm²

∴ The area of the cross-section = 60 cm²

→ Substitute the lateral area and the area of the cross-section in the rule

of the total surface area above

∵ The surface area = 500 + 2(60)

∴ The surface area = 500 + 120

∴ The surface area = 620 cm²

∴ The total surface area of the prism is 620 cm²

You might be interested in

Write an equation in slope intercept form for the line that passes through (-1, -2) and (3, 4)

LenaWriter [7]

Answer:

The slope-intercept form of the line equation is:

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where

m is the slope

b is the y-intercept

Given the points

(-1, -2)

(3, 4)

Determining the slope between (-1, -2) and (3, 4)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(3,\:4\right)$

$m=\frac{4-\left(-2\right)}{3-\left(-1\right)}$

$m=\frac{3}{2}$

Thus, the slope of the line is:

m = 3/2

substituting m = 3/2 and the point (3, 4) in the slope-intercept form of the line equation

y = mx+b

$4=\frac{3}{2}\left(3\right)+b$

switch sides

$\frac{3}{2}\left(3\right)+b=4$

$\frac{9}{2}+b=4$

subtract 9/2 from both sides

$\frac{9}{2}+b-\frac{9}{2}=4-\frac{9}{2}$

$b=-\frac{1}{2}$

now substituting m = 3/2 and b = -1/2 in the slope-intercept form of the line equation

$y = mx+b$

$y=\:\frac{3}{2}x\:+\:\left(-\frac{1}{2}\right)$

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

Therefore, the slope-intercept form of the line equation is:

$y=\:\frac{3}{2}x\:-\frac{1}{2}$

8 0

3 years ago

If you add or subtract two rational numbers, is the result sometimes, always, or never rational?

lawyer [7]

Answer:

Always

Step-by-step explanation:

8 - 9 = -1

1/3 - 1/6 = 1/6 are 2 examples

8 0

3 years ago

What is the value of h(3) multiplied by h(7)<br><br> P.S. I will give brainliest to the best answer

Eddi Din [679]

Answer:

Step-by-step explanation:

Because h(3) times h(7) is equal to 21.

Hope it helps!

4 0

3 years ago

The first steps in writing f(x) = 3x^2 -24x+10 in vertex form what is the function written in vertex form

Vika [28.1K]

F(x) = 3(x-4)^2-38 because finding the perfect square would get you f(x)+38=3(x^2-8x+16) and then finding the squareroot of that and moving the constant on the left back to the right would leave u with f(x)=3(x-4)^2-38

4 0

4 years ago

Read 2 more answers

Total health care costs in the United States in 2016 was $1.7 trillion. he US population was 290.9 million. What was the average

dusya [7]

Answer:

$5,843.9

Step-by-step explanation:

2016

Total health care cost in US = $1.7 trillion

= $1,700,000,000,000

Population in US = 290.9 million.

= 290,900,000

Average amount spent per person on health care = Total health care cost in US / Population in US

= 1,700,000,000,000 / 290,900,000

= $5843.9326228944

Approximately,

$5,843.9

To the nearest whole number

= $5,844

7 0

3 years ago