What is the area of a polygon with vertices of (-2,-4)(4,-4)(4,4) and (-5,4)?
a) 216 square units
b) 30 square units
c)120 square units
d) 60 square units
5 answers
c) 120 square units
the figure is a trapezoid, so
A = (6+9)/2 * 8 = 60
A = (6+9)/2 * 8 = 60
I'm sorry, but your answer is incorrect. The given vertices do not form a trapezoid, but rather a quadrilateral with no parallel sides. Therefore, we cannot use the formula for trapezoid area.
To find the area of this quadrilateral, we can divide it into two triangles and use the formula for triangle area. Let's label the vertices as follows:
A = (-2,-4)
B = (4,-4)
C = (4,4)
D = (-5,4)
We can see that triangle ABC is a right triangle with legs of length 6 and 8. Therefore, its area is:
A(ABC) = (1/2) * 6 * 8 = 24
Similarly, triangle ACD is also a right triangle with legs of length 9 and 8. Therefore, its area is:
A(ACD) = (1/2) * 9 * 8 = 36
The total area of the quadrilateral ABCD is the sum of the areas of triangles ABC and ACD:
A(ABCD) = A(ABC) + A(ACD) = 24 + 36 = 60
Therefore, the area of the polygon with vertices of (-2,-4)(4,-4)(4,4) and (-5,4) is 60 square units.
The correct answer is d) 60 square units
To find the area of this quadrilateral, we can divide it into two triangles and use the formula for triangle area. Let's label the vertices as follows:
A = (-2,-4)
B = (4,-4)
C = (4,4)
D = (-5,4)
We can see that triangle ABC is a right triangle with legs of length 6 and 8. Therefore, its area is:
A(ABC) = (1/2) * 6 * 8 = 24
Similarly, triangle ACD is also a right triangle with legs of length 9 and 8. Therefore, its area is:
A(ACD) = (1/2) * 9 * 8 = 36
The total area of the quadrilateral ABCD is the sum of the areas of triangles ABC and ACD:
A(ABCD) = A(ABC) + A(ACD) = 24 + 36 = 60
Therefore, the area of the polygon with vertices of (-2,-4)(4,-4)(4,4) and (-5,4) is 60 square units.
The correct answer is d) 60 square units
AB = 6
CD = 9
AB ║ CD
so it is a trapezoid.
CD = 9
AB ║ CD
so it is a trapezoid.
I apologize for my previous response. You are correct that AB and CD are parallel, making the figure a trapezoid.
To find the area of this trapezoid, we can use the formula:
A = [(b1 + b2)/2] * h
where b1 and b2 are the lengths of the parallel sides (in this case, AB and CD), and h is the height of the trapezoid (the perpendicular distance between the parallel sides).
To find the height, we can use the fact that the vertical distance between points B and C is 8 units. Therefore, the height of the trapezoid is 8 units.
Using the given lengths, we have:
A = [(6 + 9)/2] * 8 = 60
Therefore, the area of the trapezoid with vertices of (-2,-4), (4,-4), (4,4) and (-5,4) is 60 square units.
The correct answer is d) 60 square units.
To find the area of this trapezoid, we can use the formula:
A = [(b1 + b2)/2] * h
where b1 and b2 are the lengths of the parallel sides (in this case, AB and CD), and h is the height of the trapezoid (the perpendicular distance between the parallel sides).
To find the height, we can use the fact that the vertical distance between points B and C is 8 units. Therefore, the height of the trapezoid is 8 units.
Using the given lengths, we have:
A = [(6 + 9)/2] * 8 = 60
Therefore, the area of the trapezoid with vertices of (-2,-4), (4,-4), (4,4) and (-5,4) is 60 square units.
The correct answer is d) 60 square units.