You have a rectangular prism on your hands. The formula for the volume of a rectangular prism is
(B/2) • l
Where B is the area of the base, and l is the length.
If you notice, you do NOT have the height of the triangle. However, you know that it is an equilateral triangle. So, you may split the triangle into two. Once you do, you can see that it is a right triangle. It’s hypotenuse is 3. If you know your triangles, you will realize that this is a 30 60 90 triangle. Therefore, the height will be 1.5 * sqrt(3)
So, to get B...
3 * 1.5sqrt(3)
4.5sqrt(3)
(Divide by 2)
2.25sqrt(3)
O
(9sqrt(3))/4
Multiply by the length of the prism, 6
This is your final answer in fraction form
27
— 2^rt(3)
2
For starters, we know that the angle measures have to be similar or the same, since similar shapes always contain the same angle measures. We can use the way that the letters of each shape line up to identify which angle correspond to each other. Angle R should be congruent to angle W, but angle P is not congruent to N, it would be congruent to M though. Now we get to the tricky part, figuring out line segment lengths. Again using the letters in each shape, we can see that TK and NM do not correspond to each other, and thus cannot be congruent or similar. But, with RP/WM, this is correctly lined up with each other. TR/EW, same with this one, and TK/EN is also the same. With this Info, we can figure out the dilation of the smaller shape, or just figure out if they are similar or not. (So pick B. And D.)
Answer:
20 5/8 yd^2
Step-by-step explanation:
width = 3 3/4 yd
length = 5 1/2 yd
First change both measurements to fractions.
3 3/4 = 3 + 3/4 = 12/4 + 3/4 = 15/4
5 1/2 = 5 + 1/2 = 10/2 + 1/2 = 11/2
area = length * width
area = 15/4 yd * 11/2 yd
area = (15 * 11)/(4 * 2) yd^2
area = 165/8 yd^2
165/8 = 20 remainder 5
area = 20 5/8 yd^2
The <em>total surface</em> area of the three figures are 702 square feet.
<h3>How to estimate the amount of metal needed to produce a given amount of figures</h3>
According to this problem, we are required to determine the amount of metal needed to build three pieces with the dimensions presented in the figure.
In this case, we need to estimate the <em>total</em> surface area (
), in square feet, required for the production of the three pieces, that is, the product of the number of pieces (<em>n</em>), no unit, and the surface area of each piece (<em>A</em>).
Now we proceed to calculate the total surface area:
![+(5\,ft)\cdot (8\,ft)+2\cdot (3\,ft)\cdot (5\,ft) + 2\cdot (4\,ft)\cdot (2\,ft) + (3\,ft)\cdot (4\,ft) ]](https://tex.z-dn.net/?f=%2B%285%5C%2Cft%29%5Ccdot%20%288%5C%2Cft%29%2B2%5Ccdot%20%283%5C%2Cft%29%5Ccdot%20%285%5C%2Cft%29%20%2B%202%5Ccdot%20%284%5C%2Cft%29%5Ccdot%20%282%5C%2Cft%29%20%2B%20%283%5C%2Cft%29%5Ccdot%20%284%5C%2Cft%29%20%5D)
The <em>total surface</em> area of the three figures are 702 square feet. 
To learn more on surface areas, we kindly invite to check this verified question: brainly.com/question/2835293
