Answer:
19 square units
Step-by-step explanation:
Hello!
Step 1: Plot the points
We are first going to plot the points on the coordinate graph and connect the points to create a shape.
Refer to attachment titled "Step 1"
Step 2: Box the shape
Since this is an irregular shape, I'm going to make a box around the shape and subtract the area of the empty spaces to find the area of the original polygon.
Refer to attachment titled "Step 2"
Step 3: Area of Edges
We are going to find the area of the shapes A, B, and C and subtract them from the area of the big box to find the area of the polygon.
Area of a triangle = 1/2(base x height)
- Area of Box = 6 un x 7 un
- Area of Box = 42 un²
Area of A:
- Area A = 1/2(4 un x 2 un)
- Area A = 1/2(8 un²)
- Area A = 4 un²
Area of B:
- Area B = 4 un x 4 un
- Area B = 16 un²
Area of C:
- Area C = 1/2(2 un x 3 un)
- Area C = 1/2(6 un²)
- Area C = 3 un²
Step 4: Area of the polygon
Now, we can simply subtract the values of A, B, and C from the box to get the area of the polygon.
- Area Polygon = Box - A - B - C
- Area Polygon = 42 un² - 4 un² - 16 un² - 3 un²
- Area Polygon = 38 un² - 16 un² - 3 un²
- Area Polygon = 22 un² - 3 un²
- Area Polygon = 19 un²
The area of the polygon is 19 un²
-Chetan K
