Answer:
(a) The formula for the area A of a trapezoid
[tex]A = \frac{1}{2}(b_{1}+ b_{2})h[/tex]
(b) Solve the formula for h
[tex]h = \frac{2A}{b_{1}+b_{2}}[/tex]
(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
[tex]A = \frac{1}{2}(b_{1}+ b_{2})h[/tex]
(b) Solve the formula for h
As the formula for the area A of a trapezoid is
[tex]A = \frac{1}{2}(b_{1}+ b_{2})h[/tex]
So, formula for height h of trapezoid
[tex]h = \frac{2A}{b_{1}+b_{2}}[/tex]
(c) Using the new formula to find the height h of the trapezoid
Using [tex]h = \frac{2A}{b_{1}+b_{2}}[/tex] to find the height h of the trapezoid.
So,
[tex]h = \frac{2A}{b_{1}+b_{2}}[/tex]
[tex]h = \frac{2(72)}{16+8}[/tex] ∵b₁ = 16, b₂ = 8, A = 72cm²
[tex]h = \frac{144}{24}[/tex]
[tex]h = 6 cm[/tex]
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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