Figure ABCD has vertices A(−4, 1), B(2, 1), C(2, −5), and D(−4, −3). What is the area of Figure ABCD? 24 square units 30 square units 36 square units 45 square units is it C?
Well, surely you plotted the points,
and surely you must have seen that your figure is made up of
a rectangle 4 by 6 and a right-angled triangle with perpendicular sides
of 6 and 2
Find the area of each shape and add them
mathhelper thank you
To find the area of a quadrilateral, we can use the formula for the area of a trapezoid. However, since figure ABCD is a rectangle, we can use a simpler formula: Area = length × width.
Step 1: Find the length of the rectangle.
To find the length, we can use the distance formula between points A and D:
Length = √((-4 - (-4))^2 + (1 - (-3))^2)
Length = √(0^2 + 4^2)
Length = √16
Length = 4 units
Step 2: Find the width of the rectangle.
To find the width, we can use the distance formula between points A and B:
Width = √((2 - (-4))^2 + (1 - 1)^2)
Width = √(6^2 + 0^2)
Width = √36
Width = 6 units
Step 3: Calculate the area of the rectangle.
Area = Length × Width
Area = 4 units × 6 units
Area = 24 square units
Therefore, the area of figure ABCD is 24 square units. Your answer of choice C is correct.
To find the area of a figure, you can use the formula for the area of a rectangle:
Area = Length × Width
For a rectangle, the length and width can be determined using the coordinates of the vertices. In this case, the coordinates of two adjacent vertices of the rectangle are enough to determine the length and width.
Let's calculate the length of the rectangle using the coordinates of vertices A and B:
Length = Distance between A and B
Using the distance formula:
Length = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates of A(-4, 1) and B(2, 1):
Length = √[(2 - (-4))^2 + (1 - 1)^2]
Length = √[6^2 + 0^2]
Length = √[36 + 0]
Length = √36
Length = 6
Now let's calculate the width of the rectangle using the coordinates of vertices B and C:
Width = Distance between B and C
Using the distance formula:
Width = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the coordinates of B(2, 1) and C(2, -5):
Width = √[(2 - 2)^2 + (-5 - 1)^2]
Width = √[0^2 + (-6)^2]
Width = √[0 + 36]
Width = √36
Width = 6
Now that we have the length and width, we can calculate the area:
Area = Length × Width
Area = 6 × 6
Area = 36 square units
So, the correct answer is 36 square units, which matches option C.