Question

what is the missing length? 6.9 cm t area of shaded region = 27.6 cm² t = centimeters

Explanation:

Step1: Recall triangle area formula

The area of a triangle is given by \( A = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the height is \( 6.9 \, \text{cm} \), the base is \( t \), and the area \( A = 27.6 \, \text{cm}^2 \).

Step2: Substitute values into formula

Substitute \( A = 27.6 \), \( \text{height} = 6.9 \) into the formula: \( 27.6 = \frac{1}{2} \times t \times 6.9 \).

Step3: Solve for \( t \)

First, multiply both sides by 2: \( 27.6 \times 2 = t \times 6.9 \), which gives \( 55.2 = 6.9t \). Then, divide both sides by \( 6.9 \): \( t = \frac{55.2}{6.9} \). Calculate \( \frac{55.2}{6.9} = 8 \).

Answer:

\( 8 \)