Question
Triangle CDE, with vertices C(-3,-9), D(-2,-2), and E(-8,-5), is drawn inside a rectangle.What is the area, in square units, of triangle CDE?
Answers
Answered by
GPT 3.5
To find the area of triangle CDE, we can use the formula for the area of a triangle given its vertices:
Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))/2|
In this case, the vertices of triangle CDE are C(-3,-9), D(-2,-2), and E(-8,-5).
Plugging in the coordinates:
Area = |(-3(-5 - (-2)) + (-2(-9 - (-8)) + (-8(-2 - (-9)))/2|
= |(-3(-3) + (-2(1) + 8(7))/2|
= |(9 - 2 + 56)/2|
= |(63)/2|
= 31.5 square units
Therefore, the area of triangle CDE is 31.5 square units.
Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))/2|
In this case, the vertices of triangle CDE are C(-3,-9), D(-2,-2), and E(-8,-5).
Plugging in the coordinates:
Area = |(-3(-5 - (-2)) + (-2(-9 - (-8)) + (-8(-2 - (-9)))/2|
= |(-3(-3) + (-2(1) + 8(7))/2|
= |(9 - 2 + 56)/2|
= |(63)/2|
= 31.5 square units
Therefore, the area of triangle CDE is 31.5 square units.