Trapezoid Area Problem: Find Missing Base Length Given Area 67 cm²

Given that the area of the trapezoid ABCD is 67 cm².

The height of the trapezoid is 8 cm.

The length of one of the bases is 12cm

What is the length of the other base?

The problem involves finding the missing base of a trapezoid using its area. Let's solve it step by step:

• The formula for the area of a trapezoid is:

  $A = \frac{1}{2} \times (b_1 + b_2) \times h$

• We're given:

  - $A = 67 \text{ cm}^2$
  - $h = 8 \text{ cm}$
  - $b_1 = 12 \text{ cm}$

• Substitute the known values into the formula:

  $67 = \frac{1}{2} \times (12 + b_2) \times 8$

• First, simplify the equation:

  $67 = 4 \times (12 + b_2)$

• Divide both sides by 4 to isolate the sum of the bases:

  $16.75 = 12 + b_2$

• Solve for $b_2$:

  $b_2 = 16.75 - 12$ $b_2 = 4.75 \text{ cm}$

Thus, the length of the other base is $4.75 \text{ cm}$.