Find the area of the following shape. You must show all work to receive credit.
Figure ABCDEF is shown. A is located at negative 2, 6. B is located at negative 5, 2. C is located at negative 2, negative 3. D
you have a problem with writing points as pairs of coordinates?
A = (-2,6)
B = (-5,2)
C = (-2,-3)
Much easier to read.
Now, when you get around to letting us know the rest of the points, maybe you will get some help.
General polygonal shapes can always be analyzed by considering them as groups of triangles or rectangles, which are easy to work with.
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To find the area of the shape ABCDEF, we need to break it down into simpler shapes and calculate their areas separately. From the given coordinates, we can see that ABCDEF is a quadrilateral.
Step 1: Find the length of AB and CD
Using the distance formula, we can find the length of AB and CD.
Distance Formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
AB:
x1 = -2, y1 = 6 (point A)
x2 = -5, y2 = 2 (point B)
AB = sqrt((-5 - -2)^2 + (2 - 6)^2)
AB = sqrt((-3)^2 + (-4)^2)
AB = sqrt(9 + 16)
AB = sqrt(25)
AB = 5
CD:
x1 = -2, y1 = -3 (point C)
x2 = 7, y2 = 8 (point F)
CD = sqrt((7 - -2)^2 + (8 - -3)^2)
CD = sqrt((7 + 2)^2 + (8 + 3)^2)
CD = sqrt(9^2 + 11^2)
CD = sqrt(81 + 121)
CD = sqrt(202)
Step 2: Find the height of the quadrilateral
To find the height of the quadrilateral, we need to find the perpendicular distance between AB and CD. Let's call it h.
From the given coordinates, we can see that AB is parallel to the y-axis, and CD is parallel to the x-axis. Therefore, the height will be the vertical distance between AB and CD.
The y-coordinate of B is 2, and the y-coordinate of C is -3.
Height (h) = 2 - (-3) = 5
Step 3: Calculate the area of the quadrilateral
Now that we have the length of AB (5) and the height (5), we can calculate the area of the quadrilateral using the formula:
Area = (base * height) / 2
Area = (5 * 5) / 2
Area = 25 / 2
Area = 12.5
Therefore, the area of quadrilateral ABCDEF is 12.5 square units.
To find the area of the shape ABCDEF, we can break it down into smaller triangles and rectangles.
First, let's label the coordinates of the vertices:
A: (-2, 6)
B: (-5, 2)
C: (-2, -3)
D: (4, -3)
E: (4, 2)
F: (-5, 2)
To calculate the area of the shape, we can divide it into two main parts: triangle ABC and rectangle CDEF.
1. Triangle ABC:
The base of triangle ABC is the distance between point B and C, which is |-5 - (-2)| = 3 units.
The height of triangle ABC is the vertical distance between point C and A, which is |(-3) - 6| = 9 units.
Using the formula for the area of a triangle, the area of triangle ABC is (1/2) * base * height = (1/2) * 3 * 9 = 13.5 square units.
2. Rectangle CDEF:
The length of the rectangle CDEF is the distance between point C and D, which is |(-2) - 4| = 6 units.
The width of the rectangle CDEF is the distance between point C and F, which is |-5 - (-2)| = 3 units.
To find the area of the rectangle, you simply multiply the length and width: 6 * 3 = 18 square units.
Now, we add the areas of triangle ABC and rectangle CDEF to get the total area of the shape ABCDEF: 13.5 + 18 = 31.5 square units.
Therefore, the area of the shape ABCDEF is 31.5 square units.