Help find surface area please

[riri914267]

Hello, please help me find the surface area of this and correct my work.

So, here is my work
Can somebody please tell me what I did wrong?

 

[riri914267]

I got 646.28 cm^2, but I do not think that is correct.

 

[Deleted member 4993]

Hello, please help me find the surface area of this and correct my work.
View attachment 26671
So, here is my workView attachment 26672
Can somebody please tell me what I did wrong?

There are 3 rectangles. Area of each rectangle = 8 * 20

There are 2 triangles each with base = 8 cm and height = √(64-16) cm

So total area = ?

 

[lex]

We don't know what the letters stand for in your formula - but the initial formula seems to be incorrect.
All the calculations are grand up until the part where you find the area of the two triangles.
The height of the triangles is [MATH]4\sqrt{3}[/MATH], and the base is 8. The area of a triangle is [MATH]\frac{1}{2}[/MATH]base×height
Since there are two of them you might as well calculate them together and do base×height = [MATH]8 \times 4\sqrt{3}[/MATH]The mistake you made was to do [MATH]24 \times 4\sqrt{3}[/MATH]

 

[riri914267]

We don't know what the letters stand for in your formula - but the initial formula seems to be incorrect.
All the calculations are grand up until the part where you find the area of the two triangles.
The height of the triangles is [MATH]4\sqrt{3}[/MATH], and the base is 8. The area of a triangle is [MATH]\frac{1}{2}[/MATH]base×height
Since there are two of them you might as well calculate them together and do base×height = [MATH]8 \times 4\sqrt{3}[/MATH]The mistake you made was to do [MATH]24 \times 4\sqrt{3}[/MATH]

Sorry, I should mention that
S = Surface area
a = base apothem
P = perimeter
h = height
B = base area
L = lateral area

Formula to find surface Area of a right prism
S = aP + Ph
or
S = 2B + L

So, I got
4root3 for the apothem
24 for the perimeter
20 for the height

S = (4root3)(24) + (24)(20) ?

I used the formula for surface area of a right prism, is that right?
You can also use the triangle area? Please explain it to me in the surface area of a right prism formula

 

[nasi112]

[MATH]T_A = [/MATH] area of one triangle [MATH]= \sqrt{\left(\frac{8 + 8 + 8}{2}\right)\left(\frac{8 + 8 + 8}{2} - 8\right)^3} = 16\sqrt{3}[/MATH]
[MATH]R_A = [/MATH] area of one rectangle [MATH] = 8 \cdot 20 = 160[/MATH]
We have two triangles and three rectangles.

Total Surface Area [MATH] = 2T_A + 3R_A = \ ?[/MATH]

 

[lex]

I used the formula for surface area of a right prism, is that right?
You can also use the triangle area? Please explain it to me in the surface area of a right prism formula

I understand what you are doing now.
P stands for the Perimeter of the Base.
Where you went wrong is the calculation of the apothem.
In an equilateral triangle the apothem is [MATH]\tfrac{1}{3}[/MATH] the height of the triangle. So your apothem should be [MATH]\tfrac{4\sqrt{3}}{3}[/MATH]The apothem of a regular n-gon will be [MATH]\tfrac{b}{2\tan(180/n)}[/MATH] (working in degrees, and [MATH]b[/MATH] being the length of side of the base).

 

[lookagain]

riri914267, when you are given the side length of an equilateral triangle,
please skip finding the perimeter, apothem, and other related calculations.
Just substitute into the formula $\displaystyle \ A \ = \ \dfrac{s^2\sqrt{3}}{4}. \ \$ Here, for one of the

equilateral triangles, it calculates to $\displaystyle \ 16\sqrt{3} \ sq. \ cm.$