Answer:
(a) The formula for the area A of a trapezoid
![A = \frac{1}{2}(b_{1}+ b_{2})h](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28b_%7B1%7D%2B%20b_%7B2%7D%29h)
(b) Solve the formula for h
![h = \frac{2A}{b_{1}+b_{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B2A%7D%7Bb_%7B1%7D%2Bb_%7B2%7D%7D)
(c) Find the height h of the trapezoid
The height h of the trapezoid is 6 cm.
Step-by-step explanation:
(a) The formula for the area A of a trapezoid
As b₁, b₂ being the lengths of the bases and 'h' is the height.
So, the formula for the area A of a trapezoid
![A = \frac{1}{2}(b_{1}+ b_{2})h](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28b_%7B1%7D%2B%20b_%7B2%7D%29h)
(b) Solve the formula for h
As the formula for the area A of a trapezoid is
![A = \frac{1}{2}(b_{1}+ b_{2})h](https://tex.z-dn.net/?f=A%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28b_%7B1%7D%2B%20b_%7B2%7D%29h)
So, formula for height h of trapezoid
![h = \frac{2A}{b_{1}+b_{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B2A%7D%7Bb_%7B1%7D%2Bb_%7B2%7D%7D)
(c) Using the new formula to find the height h of the trapezoid
Using
to find the height h of the trapezoid.
So,
![h = \frac{2A}{b_{1}+b_{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B2A%7D%7Bb_%7B1%7D%2Bb_%7B2%7D%7D)
∵b₁ = 16, b₂ = 8, A = 72cm²
![h = \frac{144}{24}](https://tex.z-dn.net/?f=h%20%3D%20%5Cfrac%7B144%7D%7B24%7D)
![h = 6 cm](https://tex.z-dn.net/?f=h%20%3D%206%20cm)
So, h = 6 cm
Hence, The height h of the trapezoid will be 6 cm.
Keywords: area of trapezoid, length, base, height
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