For Exercises 32–35, (a) graph the lines and (b) find the area of the triangle enclosed by the lines.

32. y = x ,   x = 0   , y = 7 y equals x comma x . equals 0 comma . y equals 7
33. y = x + 2   , y = 2   , x = 6 y equals . x plus 2 comma . y equals 2 comma . x equals 6
34. y = − 1 2 x + 3   , y = 0   , x = − 2 y equals , minus , 1 half . x plus 3 comma . y equals 0 comma . x equals , negative 2
35. y = 3 4 x − 2   , y = − 2 , x = 4 y equals , 3 fourths . x minus 2 comma . y equals . negative 2 comma . x equals 4
36. Probability Your friend drew these three figures on a grid. A fly lands at random at a point on the grid.

    
    Image Long Description

    1. Writing Is the fly more likely to land on one of the figures or on the blank grid? Explain.
    2. Suppose you know the fly lands on one of the figures. Is the fly more likely to land on one figure than on another? Explain.

Coordinate Geometry Find the area of a polygon with the given vertices.

37. A ( 3 ,   9 ) , B ( 8 ,   9 ) ,   C ( 2 , − 3 ) , D ( − 3 , − 3 ) eh open 3 comma 9 close comma b open 8 comma 9 close comma c open 2 comma negative 3 close comma . d open negative 3 comma . negative 3 close
38. E(1, 1), F(4, 5), G(11, 5), H(8, 1)
39. D(0, 0), E(2, 4), F(6, 4), G(6, 0)
40. K ( − 7 , − 2 ) , L ( − 7 ,   6 ) , M ( 1 ,   6 ) ,   N ( 7 , − 2 ) k open negative 7 comma . negative 2 close comma . l open negative 7 comma 6 close comma . m open 1 comma 6 close comma n open 7 comma negative 2 close

Find the area of each figure.

C Challenge

History The Greek mathematician Heron is most famous for this formula for the area of a triangle in terms of the lengths of its sides a, b, and c.

A = s ( s − a ) ( s − b ) ( s − c ) , where  s = 1 2 ( a + b + c ) eh equals . square root of s open s minus eh close open s minus b close open s minus c close end root . comma , where , s equals , 1 half , open eh plus b plus c close

Use Heron's Formula and a calculator to find the area of each triangle. Round your answer to the nearest whole number.

44. a = 8   in. , b = 9   in. , c = 10   in. eh equals 8 in. comma . b equals 9 in. comma . c equals 10 in.
45. a = 15   m , b = 17   m , c = 21   m eh equals 15 m comma b equals 17 m comma c equals 21 m
46. 1. Use Heron's Formula to find the area of this triangle.

    2. Verify your answer to part (a) by using the formula A = 1 2 b h . eh equals . 1 half , b h .

       

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