Answer:
A) 24 ft³
Step-by-step explanation:
The area of the right triangle base is ...
A = (1/2)(3)(4) = 6 ft²
The volume of the triangular prism is the product of the area of its base (6 ft²) and its height (4 ft).
V = Bh = (6 ft²)(4 ft) = 24 ft³ . . . . matches choice A
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<em>Comment on the triangle</em>
You know the 3-4-5 triangle is a right triangle, because you have seen those numbers many times in relation to the Pythagorean theorem. If you don't know that, then you can check to see by using the Pythagorean theorem:
5² = 3² +4²
25 = 9 + 16 . . . . . true; so the triangle is a right triangle
In any event, there are other means for finding the area of the triangle based on the lengths of its sides. You will get the same area result.
Using Heron's formula, s = (a+b+c)/2 = (3+4+5)/2 = 6.
A = √(s(s -a)(s -b)(s -c)) = √(6(3)(2)(1)) = √36 = 6 . . . . area of base triangle
Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
The expression for the area of the triangle is,
![\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Csqrt%5B%5D%7Bs%28s-p%29%28s-q%29%28s-r%29_%7B%7D%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B21.5%5Ctext%7B%20in%2821.5%20in-13%20in%29%2821.5%20in-18%20in%29%2821.5%20in-12%20in%29%7D%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%2821.5%5Ctext%7B%20in%29%288.5%20in%29%283.5%20in%29%289.5%20in%29%7D%7D%20%5C%5C%20%3D77.95in%5E2%20%5Cend%7Bgathered%7D)
Thus, the area of the given triangle is 77.95 sq-inches.
Answer:
67%
Step-by-step explanation:
I did math counts
Answer:
Length is 38 and Width is 19
Step-by-step explanation:
