Find the surface area of a prism with height of 4 m when its base is an equilateral triangle with sides of 6 m

Question

please help me

Answer 1

Hey there!

We need to use the formula S=2B+Ph, in order to find the surface area of the prism.

In the formula S=2B+Ph, B is the area of the base, P is the perimeter of the base and h is the height of the prism.

We know that B=1/2aP, where a is the apothem of the base and P is the perimeter of the base.

Substituting that into the formula, we get.

S=aP+Ph or S=P(a+h).

In order to find the value for a, we need to use the Pythagorean Theorem i.e. a^2+(s/2)^2=s^2.

The sides of the equilateral triangle is 6. Substituting that for s, we get,

a^2+(s/2)^2=s^2 -->
a^2+(6/2)^2=6^2 -->
a^2+3^2=6^2 -->
a^2+9=36 -->
a^2=27 -->
a=sqrt(27) -->
a=3sqrt(3).

Now let's find P.

P=ns -->
P=(3)(6) -->
P=18.

In the formula P=ns, n is the number of sides in the polygon and s is the side length. We can now find the surface area of a prism.

S=P(a+h) -->
S=18(3sqrt(3)+4) -->
S=54sqrt(3)+72 -->
S=72+54sqrt(3)

So the surface area of the prism is 72+54sqrt(3) cm^2 or about 165.53 cm^2.

Hope it helps!

Answer 2

1. figure the height of the triangle Since the hypotenuse squared = the sum of the squares of the other two legs you have 8 squared = 4(1/2 of one side) squared + x squared. Solve for x and you will know the height of the triangle. 2. the area of a triangle is = to 1/2 base time height. So the area of the triangle = (8 (base) * height (x)) divided by 2 3. The surface area of the prism can be found by adding the area of the top and bottom triangles + the surface area of for the three sides. The surface area of one side = 8 time 12 The sum of the area of three side and the surface area of the tow triangles = the total surface area. 4. To find the volume of the prism take the surface area of one triangle and multiply it time the height of the prism. this is equal to ..... Surface area of one triangle times 12 the height. The answers will all be in square inches or cubic inches. Hope this helps1

Answer 3

OK Monica, you have 5 shapes whose areas you have to find and add up. 3 of these are rectangles of length 6m and height 4m. The other 2 are the equilateral trianges. To find their area without the dreadful perimeter formula, We divide each triangle into 2 30/60/90 triangles. The base of each will be 3 and the height will be (3/2)sqrt(3) meters. For two of these triangles on one side and the two on the other side, the TOTAL triangular area will be
4*(1/2)*(3/2)sqrt(3)*3.
So do the math and add up the areas.

Answer 4

The (side surface) is (perimeter of the triangle) * (hight of the prism) = (6m*3)*4m = 72 m^2

Than I have to add the top and bottom surfaces which are teh surface of the equilateral triangle.

As in an equilateral triangle the hight is (sqrt(3)/4) * L^2 you find
(triangle surface) = 15.58845..

So the total surface is
(side surface) + (triangle surface*2) = 103.1769..

Answer 5

"height" of a base...
=sqrt(6^2 - 3^2) = 3sqrt(3)

height of a prism... = 4.

there are 3 congruent faces and one equilateral base.

so...
3(4*6/2) + [3sqrt(3)](6/2)
= 36 + 9sqrt(3)

that's my answer...

Answer 6

base surface area = 3sqrt(27)
1 side of the prism = 3sqrt(29.5)
3 side = 3x3sqrt(29.5)=9sqrt(29.5)
total surface = 9sqrt(29.5)+3sqrt(27)