Question

3 (grid with a pentagon, handwritten 4/4, 2, 4, and a blank line)

Explanation:

To find the area of the pentagon, we can divide it into a triangle and a trapezoid.

Step 1: Area of the Triangle

The base of the triangle is \( 4 \) (from the grid) and the height is \( 2 \).
The formula for the area of a triangle is \( A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} \).
Substituting the values:
\( A_{\text{triangle}} = \frac{1}{2} \times 4 \times 2 = 4 \).

Step 2: Area of the Trapezoid

The trapezoid has bases \( b_1 = 4 \) (bottom base) and \( b_2 = 2 \) (top base, same as the base of the triangle), and height \( h = 2 \).
The formula for the area of a trapezoid is \( A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h \).
Substituting the values:
\( A_{\text{trapezoid}} = \frac{1}{2} \times (4 + 2) \times 2 = \frac{1}{2} \times 6 \times 2 = 6 \).

Step 3: Total Area of the Pentagon

Add the area of the triangle and the trapezoid:
\( A_{\text{total}} = A_{\text{triangle}} + A_{\text{trapezoid}} = 4 + 6 = 10 \).

Answer:

The area of the pentagon is \( \boldsymbol{10} \) (assuming each grid square has an area of 1).