Question

what is the area of the shaded region? write your answer as a whole number or a decimal rounded to the nearest hundredth. square centimeters

Explanation:

Step1: Calculate area of outer triangle

The outer triangle has base \( 17 \) cm and height \( 18 \) cm. The formula for the area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \). So, \( A_{\text{outer}} = \frac{1}{2} \times 17 \times 18 \).
\( A_{\text{outer}} = 9 \times 17 = 153 \) \( \text{cm}^2 \).

Step2: Calculate area of inner triangle

The inner triangle has base \( 10 \) cm and height \( 12 \) cm. Using the same triangle area formula, \( A_{\text{inner}} = \frac{1}{2} \times 10 \times 12 \).
\( A_{\text{inner}} = 5 \times 12 = 60 \) \( \text{cm}^2 \).

Step3: Subtract inner area from outer area

The area of the shaded region is \( A_{\text{shaded}} = A_{\text{outer}} - A_{\text{inner}} \).
\( A_{\text{shaded}} = 153 - 60 = 93 \) \( \text{cm}^2 \).

Answer:

93 square centimeters