Question

which sentence describes a way to determine the area of the polygon shown? find the area of a rectangle and then subtract the area of a triangle. find the area of the shaded polygon. area of polygon = \square square units

Explanation:

Step1: Identify the polygon type

The polygon is a trapezoid (or can be seen as a rectangle plus a triangle, or a rectangle minus a triangle? Wait, actually, looking at the grid, let's count the bases and height. The top base is 3 units, bottom base is 6 units? Wait, no, looking at the grid, the figure is a trapezoid with bases of length 3 and 6, and height 4? Wait, no, maybe better to split into a rectangle and a triangle. The rectangle part: width 3, height 4. The triangle part: base (6 - 3)=3, height 4. Wait, no, let's count the squares. Alternatively, use the formula for the area of a trapezoid: \( A=\frac{(b_1 + b_2)}{2}\times h \). Here, \( b_1 = 3 \), \( b_2 = 6 \), \( h = 4 \)? Wait, no, looking at the grid, the vertical height (distance between the two parallel sides) is 4 units? Wait, no, the figure: the left side is vertical, length 4. The top is horizontal, length 3. The bottom is horizontal, length 6. The right side is a slant. So it's a trapezoid with bases 3 and 6, height 4. So area is \( \frac{(3 + 6)}{2}\times4=\frac{9}{2}\times4 = 18 \). Alternatively, split into a rectangle (3x4=12) and a triangle (base 3, height 4: \( \frac{3\times4}{2}=6 \)), so total 12 + 6 = 18.

Step2: Calculate the area

Using the trapezoid formula: \( A=\frac{(b_1 + b_2)}{2}\times h \), where \( b_1 = 3 \), \( b_2 = 6 \), \( h = 4 \). So \( A=\frac{3 + 6}{2}\times4=\frac{9}{2}\times4 = 18 \). Or rectangle (34=12) + triangle (34/2=6) = 18.

Answer:

18