4089
explanation
3(2043)+7(2043)-28+31-8(2043)
6129+14,301-28+31-16344
20,430-28+31-16344
20,402+31-16344
20,433-16344
4089
Answer:
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Step-by-step explanation:
<h3>Given:</h3>
- w= 6 units
- h= 6 units
- l= 10 units
<h3>Note that:</h3>
- w: width
- h: height
- l: length
<h3>To find:</h3>
- The volume of the given triangular prism.
<h3>Solution:</h3>
- Triangular prism is a 3 sided prism with same area of cross section with 2 triangular bases.
Let's solve!
First, let's multiply width and height.
Now, we'll have to divide the answer by 2.
Then, multiply the answer by length.
<u>Hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>triangular</u><u> </u><u>prism</u><u> </u><u>is</u><u> </u><u>1</u><u>8</u><u>0</u><u> </u><u>cubic</u><u> </u><u>units</u><u>.</u>
The enclosed shape is that of a trapezoid. The area of a trapezoid is the product of the height of it (measured perpendicular to the parallel bases) and the average length of the two parallel bases. The formula is generally written ...
... A = (1/2)(b₁ + b₂)·h
Here, the base lengths are the y-coordinates at x=4 and x=9. The height is the distance between those two x-coordinates: 9 - 4 = 5.
You are expected to find the y-values at those two points, then use the formula for the area of the trapezoid.
You can save a little work if you realize that the average of the two base lengths is the y-coordinate corresponding to the average x-coordinate: (9+4)/2 = 6.5. That is you only need to find the y-coordinate for x=6.5 and do the area math as though you had a rectangle of that height and width 5.
Going that route, we have
... y = 2(6.5) - 1 = 13 - 1 = 12
Then the trapezoid's area is
... A = 12·5 = 60 . . . . square units.