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Sagot :
Answer:
The height is equal to 10.
Step-by-step explanation:
With an isosceles trapezoid, the two legs are the same, and then the two bases. There are 2 sides given that are the same: 25. So now we know that the two legs are 25, and the two bases are 16 and 30 (doesn't really matter which length goes with which base).
To find the volume of an isosceles trapezoid, you need to use the formula [tex]\frac{30+16}{2}[/tex] · [tex]h_{1}[/tex] · [tex]h_{2}[/tex].
- You have to find the average of the bases in the trapezoid
- After that, you have to multiply the average by the trapezoid height
- After mutliplying by the trapezoid height, you need to multiply the whole thing by the prism height, which we need to find
So, to find [tex]h_{1}[/tex], which is the trapezoid height, we need to use the Pythagorean Theorem. We know that the bottom base is 30, so when we draw altitudes from the top base to the bottom base, they are the heights of the trapezoid. The two triangles formed from the altitudes are congruent (I could prove it but just trust me that they are). The rectangle that formed has the top and bottom sides equalling 16. So now we know that the triangles that were formed have bases of 7 because of Part-Whole Postulate (PWP). Since the sides are given as 25, we can find the missing side, which happens to be the height of the triangle, using the Pythagorean Theorem.
The equation would be: [tex]7^{2} +h^{2} =25^{2}[/tex]. If you do that math, you get [tex]49+h^{2} =625[/tex] after simplifying. Now you bring the 49 to the other side and subtract, leaving you with [tex]h^{2} =576[/tex]. Now you have to square root both sides, and you should end up with h=24.
Now that we know the height, we can substitute it: [tex]\frac{30+16}{2}[/tex] · [tex]h_{1}[/tex] · [tex]h_{2}[/tex] =5520 turns into
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