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3 years ago

Find the surface area of the prism

Mathematics

1 answer:

AfilCa [17]3 years ago

4 0

Answer:

156 $in^2$

Step-by-step explanation:

find the areas of all the faces and add them up

area of a rectangle: $bh$

area of a trapezoid: $\frac{1}{2} (b_1 + b_2)(h)$

$(5*3)+(6*3)+(5*3)+(3*12)+2(\frac{1}{2}*(6+12)*4) \\=15+18+15+36+2(\frac{1}{2}*18*4)\\=84+2(36)\\=156$

the area of the trapezoid is multiplied by 2 because there's a top and bottom

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Given two points $(x_1,y_1)$ and $(x_2,y_2)$ , their distance is given by:

$D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

In this problem, the formula is used to find the distance covered on each tour, hence:

$d_{AB} = \sqrt{(400 - 0)^2 + (300 - 0)^2} = 500$

$d_{BC} = \sqrt{(-800 - 400)^2 + (800 - 300)^2} = 1300$

$d_{CD} = \sqrt{(-800 - (-800))^2 + (0 - 800)^2} = 800$

$d_{DA} = \sqrt{(0 - (-800))^2 + (0 - 0)^2} = 800$

Then, the total distance is given by the sum of each separate distance, hence:

$d = d_{AB} + d_{BC} + d_{CD} + d_{DA} = 500 + 1300 + 800 + 800 = 3400$

The total distance covered on the tour is of 3400 miles.

You can learn more about distance between two points at brainly.com/question/25929988

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