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

Assume each grid is 1 unit. The rectangle has length \( l = 4 \) units and width \( w = 3 \) units. Area of rectangle: \( A_{rect} = l \times w = 4 \times 3 = 12 \) square units.

Step2: Determine triangle dimensions

The triangle has base \( b = 4 \) units (same as rectangle's length) and height \( h = 3 \) units (same as rectangle's width? Wait, no—wait, looking at the figure, the triangle's height: from the dashed line to the top, let's say height is 3? Wait, no, maybe the rectangle is 4x3, triangle base 4, height 3? Wait, area of triangle: \( A_{tri} = \frac{1}{2} \times b \times h \). If base is 4, height is 3, then \( A_{tri} = \frac{1}{2} \times 4 \times 3 = 6 \) square units.

Step3: Total area of figure

Add rectangle and triangle areas: \( A_{total} = 12 + 6 = 18 \) square units. Wait, maybe I miscalculated. Wait, let's recheck. Suppose the rectangle is 4 units long (horizontal) and 3 units tall (vertical). The triangle is on top, with base 4 and height 3? Wait, no, maybe the rectangle is 4x3 (area 12), triangle base 4, height 3? Then triangle area is 6, total 18. Alternatively, maybe the rectangle is 4x3, triangle base 4, height 3? Wait, maybe the grid: let's count the squares. The rectangle: length 4, width 3 (so 43=12). The triangle: base 4, height 3 (since from the dashed line to the top, it's 3 units? Wait, no, maybe the height is 3? Wait, area of triangle is (baseheight)/2. If base is 4, height is 3, then (4*3)/2=6. Then total area: 12+6=18.

Answer:

Area of the rectangle: 12 square units
Area of the triangle: 6 square units
Area of the figure: 18 square units