Question

find the area of this figure.
a = \square in$^2$

Explanation:

Step1: Calculate area of rectangle

The rectangle has length 12 in and height 5 in. Area of rectangle is \( length \times height \), so \( 12 \times 5 = 60 \) \( in^2 \).

Step2: Calculate base of triangle

The base of the triangle is \( 12 - 5 - 5 = 2 \) in (subtracting the two 5 in segments from the rectangle's length).

Step3: Calculate area of triangle

The triangle has base 2 in and height 6 in. Area of triangle is \( \frac{1}{2} \times base \times height \), so \( \frac{1}{2} \times 2 \times 6 = 6 \) \( in^2 \).

Step4: Sum areas of rectangle and triangle

Total area is \( 60 + 6 = 66 \) \( in^2 \).

Answer:

66