Class Examples
Plot the points for each shape. Then determine the area of the polygons.
1.
X (-10, 2), Y (-3, 2) and Z (-3, 6).
Z
Right Triangle:
4 units
X
Y
A = bh/2
A = 4*7/2
A = 14 units2
7 units
2.
E (5, 7), F (9, -5) and G (1, -3)
Scalene Triangle
A1 = bh/2
A1 = 10*4/2
A1 = 20 units2
E
1
2
A2 = bh/2
A2 = 12*4/2
A2 = 24 units2
G
3
F
A3 = bh/2
A3 = 2*8/2
A3 = 8 units2
Total Area =
AR = lw
AR = 8*12
AR = 96 units2
A1 + A2 + A3 =
20 + 24 + 8 =
52 units2
96 – 52 =
44 units2
3.
A (1, 3), B (2, 8), C (8, 8), D (10,3) and E (5, -2)
Pentagon (one possible solution)
B
E
4
3
1
A
E
2
E
A1 = lw
A1 = 6*5
A1 = 30 units2
Total Area =
A1 + A2 + A3 + A4 =
30 + 22.5 + 2.5 + 5 =
60 units2
A2 = bh/2
A2 = 9*5/2
A2 = 22.5 units2
A3 = bh/2
A3 = 1*5/2
A3 = 2.5 units2
A4 = bh/2
A4 = 2*5/2
A4 = 5 units2
4.
The vertices of a rectangle are (8, -5) and (8, 7). If the area of the rectangle is 72 square units, name the possible
location of the other two vertices.
|-5| + |7| = 12 (length of one side)
A = lw
72 = 12w
72/12 = 12w/12
6=w
5.
Since we found that the width equals 6 we can use the coordinate points we already
have to find the other possible vertices. (8, -5) and (8, 7) form a vertical line segment so
we need to find a parallel line segment to create our rectangle. To do this we can use
the same y-coordinates, but we need to find new x-coordinates. The x-coordinate 8
plus 6 equals 14 so the other two vertices could be (14, 7) and (14, -5). The xcoordinate 8 minus 6 equals 2 so the other two vertices could be (2, 7) and (2, -5)
A triangle with vertices located at (5, -8) and (5, 4) has an area of 48 square units. Determine one possible location
of the other vertex.
|-8| + |4| = 12 (length of the base)
A = bh/2
48 = 12h/2
2*48 = (12h/2)*2
96 = 12h
96/12 = 12h/12
8=h
Since we found that the height equals 8 we can use the coordinate points we already
have to find the other possible vertex. (5, -8) and (5,4) form a vertical line segment
which is the triangle’s base. If we find the midpoint of the base, we can easily find the
height at a 90 degree angle from the base. The base is 12units. 12/2 = 6 so the
midpoint would be 6 units from of the vertices. Let’s use -8. -8 + 6 = -2. The midpoint
of the base is at (5, -2). Now we know that the y-coordinate of our vertex is -2. To find
the new x-coordinates we have to add or subtract the height (8) to or from the current
x coordinate (5). 5+8 = 13 so one vertex could be (13, -2). 5-8 = -3 so the other vertex
could be (-3, -2).