Geometry Notes
9-4 Perimeter and Area in the Coordinate Plane
Ex. 1: Estimate the area of the irregular shape.
Whole squares: 21
Other pieces make up: 3.5
Total: About 24.5 square units
Ex. 2: Draw and classify the polygon with vertices A(-4, 1), B(2, 4), C(4, 0), and D(-2, -3).
Then find the perimeter and the area.
Rectangle
B
AB =
32 + 62 =
45 = 3 5
BC =
22 + 4 2 =
20 = 2 5
A
C
AB = CD and BC = AD
P = 3 5 + 2 5 + 3 5 + 2 5 = 10 5 ≈ 22.36
(
)(
)
A = lw = 3 5 2 5 = 6⋅ 5 = 30
€
D
Ex. 3: Find the area of the polygon with vertices (-2, 1), (-2, 3), (0, 3) and (1, 0).
Make a square around the shape.
Area of the square: (3)(3) = 9
Area of the triangle on the right:
1
(1)( 3) = 1.5
2
Area of the triangle on the bottom:
€
1
(1)( 3) = 1.5
2
Area of the shape: 9 – 1.5 – 1.5 = 6
€
Ex. 4: Find the area of the polygon with vertices (-1, -1), (-2, 1), (3, 2) and (2, -2).
Make a rectangle around the shape.
Area of the rectangle: (5)(4) = 20
There are 4 triangles and 1 square around
the shape.
Area of top triangle:
1
(1)(5) = 2.5
2
1
(1)( 4) = 2
2
€ triangle: 1 (1)( 3) = 1.5
Area of bottom
2
1
Area of left €
triangle: (1)(2) = 1
2
Area of right triangle:
Area of square:€(1)(1) = 1
Area of the€shape: 20 – 2.5 – 2 – 1.5 – 1 – 1 = 12