Question

A. Write the formula for the area A of a trapezoid. Use b1 and b2 for the lengths of the bases, and use h for the height.

Answer 1

Answer:

(a) The formula for the area A of a trapezoid

                 $A = \frac{1}{2}(b_{1}+ b_{2})h$

(b) Solve the formula for h

                 $h = \frac{2A}{b_{1}+b_{2}}$

(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

$A = \frac{1}{2}(b_{1}+ b_{2})h$

(b) Solve the formula for h

As the formula for the area A of a trapezoid is  

$A = \frac{1}{2}(b_{1}+ b_{2})h$

So, formula for height h of trapezoid

$h = \frac{2A}{b_{1}+b_{2}}$

(c) Using the new formula to find the height h of the trapezoid

Using  $h = \frac{2A}{b_{1}+b_{2}}$ to find the height h of the trapezoid.

So,

$h = \frac{2A}{b_{1}+b_{2}}$

$h = \frac{2(72)}{16+8}$ ∵b₁ = 16, b₂ = 8, A = 72cm²

$h = \frac{144}{24}$

$h = 6 cm$

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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