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Chapter 6: Problem 45

Find the area of the triangle with the given vertices. Round to the nearest square unit. $$(-3,-2),(2,-2),(1,2)$$

Short Answer

Expert verified
The area of the triangle is 10 square units.

Step by step solution

01

Calculate Base Length

Determining the distance between (-3, -2) and (2, -2), as they have the same y coordinates, will be simpler and considered as the base of the triangle. The distance formula is \(d = \sqrt{{(x2-x1)}^2 + {(y2-y1)}^2}\). But for our base, y-coordinates are same. So it becomes \(d = \sqrt{{(2 -(-3))}^2} = 5\).
02

Calculate Height Length

Similarly, the distance from (2, -2) to (1, 2) will be calculated as the height of the triangle. Here, x coordinates are closer to each other but y coordinates are different. So, \(d = \sqrt{{(2-2)}^2 + {(2 -(-2))}^2} = 4\).
03

Calculate the Area

Use the area formula (Area = 1/2*base*height) for the triangle using the lengths of base and height calculated earlier. Which gives the area as \(Area = 0.5*5*4 = 10\).

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