Question

what is the area of the shaded region?
26 cm
13 cm
12 cm
25 cm
write your answer as a whole number or
a decimal rounded to the nearest
hundredth.

Explanation:

Step1: Find area of large triangle

The large triangle has base \( 25 \, \text{cm} \) and height \( 26 \, \text{cm} \). The formula for the area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
So, area of large triangle: \( \frac{1}{2} \times 25 \times 26 = 325 \, \text{cm}^2 \)

Step2: Find area of small triangle

The small triangle has base \( 12 \, \text{cm} \) and height \( 13 \, \text{cm} \) (since it's a right triangle, legs are base and height). Using the same area formula:
Area of small triangle: \( \frac{1}{2} \times 12 \times 13 = 78 \, \text{cm}^2 \)

Step3: Subtract areas to get shaded region

Shaded area = Area of large triangle - Area of small triangle
\( 325 - 78 = 247 \, \text{cm}^2 \)

Answer:

\( 247 \)