Question

find the area of the figure. hint: separate into regular shapes and combine the areas! a = ? in² area formulas: rectangle ((b \times h)) and triangle ((\frac{b \times h}{2})). the figure (diagram) has 12 in measurements (top length, vertical heights, base segments).

Explanation:

Step1: Identify regular shapes

The figure can be separated into a rectangle and two triangles. The rectangle has length \( 12 \) in and height \( 12 \) in. Each triangle has base \( 12 \) in and height \( 12 \) in.

Step2: Calculate area of rectangle

Using the formula for the area of a rectangle \( A_{rectangle} = b \times h \), where \( b = 12 \) and \( h = 12 \).
\( A_{rectangle} = 12 \times 12 = 144 \) \( \text{in}^2 \)

Step3: Calculate area of one triangle

Using the formula for the area of a triangle \( A_{triangle} = \frac{b \times h}{2} \), where \( b = 12 \) and \( h = 12 \).
\( A_{triangle} = \frac{12 \times 12}{2} = 72 \) \( \text{in}^2 \)

Step4: Calculate total area of two triangles

Since there are two identical triangles, total area of triangles is \( 2 \times 72 = 144 \) \( \text{in}^2 \)

Step5: Combine areas

Total area \( A = A_{rectangle} + A_{triangles} = 144 + 144 = 288 \) \( \text{in}^2 \)

Answer:

\( 288 \)