Question

11th grade geometry:

triangle SBA has coordinates S(15,-8),B(-2,21), and A(0,0). if the height of the triangle for the corresponding base SB is 8.89 units, then determine the perimeter and area of triangle SBA. Round your answer to the nearest unit

Answer 1

The perimeter is 72 units and the area is 149 square units.

Explanation:

`\triangle SBA` has coordinates
`S(15,-8),B(-2,21)` and
`A(0,0)`

Using the distance formula.........

Length of side
`SB = √((15+2)^2+(-8-21)^2)= √(17^2+(-29)^2)= √(1130)`

Length of side
`BA= √((-2)^2+(21)^2)= √(445)`

Length of side
`AS =√((15)^2+(-8)^2)=√(289)=17`

So, the perimeter of the triangle will be:
`(SB+BA+AS)= √(1130)+ √(445)+17 =71.71... \approx 72` units. (Rounded to the nearest unit)

The height of the triangle for the corresponding base
`SB` is 8.89 units.

Formula for the Area of triangle,
`A= (1)/(2)(base* height)`

So, the area of the
`\triangle SBA` will be:
`(1)/(2)(√(1130)* 8.89)= 149.42... \approx 149` square units. (Rounded to the nearest unit)