Question

find the area of the figure below by first finding the areas of the rectangle and triangle. 1 unit area of the rectangle: square units area of the triangle: square units area of the figure: square units

Explanation:

Step1: Determine rectangle dimensions

From the grid, the rectangle has length \( l = 4 \) units and width \( w = 3 \) units. The area of a rectangle is \( A_{rectangle}=l\times w \).
\( A_{rectangle}=4\times3 = 12 \) square units.

Step2: Determine triangle dimensions

The triangle has base \( b = 4 \) units (same as rectangle length) and height \( h = 2 \) units (vertical grid units). The area of a triangle is \( A_{triangle}=\frac{1}{2}\times b\times h \).
\( A_{triangle}=\frac{1}{2}\times4\times2 = 4 \) square units.

Step3: Find total figure area

Add the area of the rectangle and the triangle: \( A_{total}=A_{rectangle}+A_{triangle} \).
\( A_{total}=12 + 4 = 16 \) square units.

Answer:

• Area of the rectangle: \( 12 \) square units
• Area of the triangle: \( 4 \) square units
• Area of the figure: \( 16 \) square units