To find the area of the polygon defined by points $A(0, -5)$, $B(3, -2)$, $C(6, -2)$, and $D(9, -5)$, we first identify the shape.
1.
Identify the Shape:
* Plotting the points shows that side $BC$ connects $(3, -2)$ and $(6, -2)$. This is a horizontal line segment with length $6 - 3 = 3$.
* Side $AD$ connects $(0, -5)$ and $(9, -5)$. This is also a horizontal line segment with length $9 - 0 = 9$.
* Since sides $BC$ and $AD$ are both horizontal, they are parallel to each other.
* A quadrilateral with exactly one pair of parallel sides is a
trapezoid.
2.
Find the Dimensions:
*
Base 1 ($b_1$): The length of the top side $BC$ is $3$ units.
*
Base 2 ($b_2$): The length of the bottom side $AD$ is $9$ units.
*
Height ($h$): The height is the vertical distance between the two parallel bases. The y-coordinate of the top base is $-2$, and the y-coordinate of the bottom base is $-5$.
$$h = |-2 - (-5)| = |-2 + 5| = 3 \text{ units}$$
3.
Calculate the Area:
* The formula for the area of a trapezoid is:
$$\text{Area} = \frac{(b_1 + b_2) \times h}{2}$$
* Substitute the values we found:
$$\text{Area} = \frac{(3 + 9) \times 3}{2}$$
$$\text{Area} = \frac{12 \times 3}{2}$$
$$\text{Area} = \frac{36}{2}$$
$$\text{Area} = 18$$
The calculated area is 18 square units.
Final Answer:
18 units²
Parent Tip: Review the logic above to help your child master the concept of polygons in the coordinate plane worksheet.
