Answer:
The answer to your question is:
Perimeter = 26.5 units
Area = 22.5 units²
Step-by-step explanation:
Data
A (5, 9)
B (8, 0)
C (0, 9)
Formula
d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
dAB = [tex]\sqrt{(8 - 5)^{2} + (0 - 9)^{2} }[/tex]
dAB = [tex]\sqrt{3^{2} + 9^{2} }[/tex]
dAB = [tex]\sqrt{90}[/tex]
dBC = [tex]\sqrt{(0 - 8)^{2} + (9 - 0)^{2} }[/tex]
dBC = [tex]\sqrt{8^{2} + 9^{2} }[/tex]
dBC = [tex]\sqrt{145}[/tex]
dAC = [tex]\sqrt{(0 - 5)^{2} + (9 - 9)^{2} }[/tex]
dAC = [tex]\sqrt{5^{2} + 0^{2} } \\[/tex]
dAC = [tex]\sqrt{25} = 5[/tex]
Perimeter = [tex]\sqrt{90} + \sqrt{145} + 5[/tex]
Perimeter = 26.5 units
Area = 1/2 [ ( 5x0) + (8x9) + (0 x 9) - (5x 9) - (0x 0) - (8x9)]
= 1/2 [ 0 + 72 + 0 - 45 - 0 - 72]
= 1/2 [-45]
= 45/2
= 22.5 units²
