Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. the height of the prism is 10 in

The surface area = 211.2 inches²

Step-by-step explanation:

* Lets explain how to solve the problem

- The prism has triangular base

- The base is equilateral triangle

- The surface area of any prism = lateral area + 2 base area

- The lateral area = perimeter of base × its height

- The perimeter of the equilateral triangle = 3L , where L is the length

 of its side

∴ The lateral area = 3L × h = 3Lh

- Area of the equilateral triangle = 1/2 × L × L × sin(60)

 Area of the equilateral triangle = 1/2 × L × L × √3/2

 Area of the equilateral triangle = √3/4 L²

∴ The surface area = 3Lh + 2(√3/4 L²) = 3Lh + √3/2 L²

∵ The side length (L) of the equilateral Δ = 6 inches

∵ The height (h) of the prism = 10 inches

∴ The surface area = 3(6)(10) + √3/2(6²)

∴ The surface area = 180 + 18√3 = 211.18

* The surface area = 211.2 inches²

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

hi! i think the answer is 1/2 : )