Answer:
7) perimeter = 16 units; area = 12 square units
8) perimeter = 8 +√13 +√29 ≈ 17.0 units; area = 8 square units
Explanation:
You want the perimeter and area of figures defined by their coordinates.
7) Quadrilateral
The figure is the brown rectangle in the attachment. It is seen to have a width of 2 units and a height of 6 units. The perimeter and area formulas are ...
P = 2(W+H) = 2(2+6) = 16 . . . . units
A = WH = (2)(6) = 12 . . . . square units
The perimeter of the figure is 16 units; the area is 12 square units.
8) Triangle
The figure is the blue triangle in the attachment. It is seen to have a base length of 8 units, and a height of 2 units. Vertex T is 3 units from one end of the triangle, and 5 units from the other end.
The lengths of the sides can be found from the distance formula:
d = √((x2 -x1)² +(y2 -y1)²)
For side ST, its length is ...
d = √((3 -0)² +(-2 -0)²) = √(9 +4) = √13 ≈ 3.606
For side TU, the side length is ...
d = √((8 -3)² +(0 -(-2))²) = √(25 +4) = √29 ≈ 5.385
Side length SU can be seen to be 8 units with no calculation required.
The perimeter is the sum of the side lengths:
ST +TU +UT = 3.606 +5.385 +8.000 = 16.991 ≈ 17.0 . . . . units
The area formula is
A = 1/2bh
A = 1/2(8)(2) = 8 . . . . square units
The perimeter of the figure is about 17.0 units; the area is 8 square units