The coordinates of the vertices of a quadrilateral are given below .
(2, 3) (8, 3)
(8, 11)
(11, 7)
What is the area, in square units, of the quadrilateral?
easiest algorithm for area of any polygon:
list the points in a column going counterclockwise, repeat the first point listed:
area = (1/2)(downproducts - upproducts)
8 11
2 3
8 3
11 7
8 11
area = (1/2)(24+6+56+121 - (22+24+33+56))
= 36
DRAW IT !!!!!
First the triangle on the left
(2,3), (8,3), (8,11)
base = 6, altitude = 8
so area = 3*8 = 24
Now the right side, the hard part
First rectangle
(8,3)(8,11)(11,11)(11,3)
that area = 3*8 = 24
subtract the triangles top and bottom
top is (8,11)(11,7)(11,11)
area top = 2*3 = 6
bottom is (8,3)(11,3)(11,7)
area bottom = 2*3 = 6
so
area right = 24 - 12 = 12
and in the end
24 + 12 = 36
To find the area of a quadrilateral, we can use the shoelace formula. The shoelace formula states that the area of a polygon with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) is given by:
Area = |(x1 * y2 + x2 * y3 + x3 * y4 + x4 * y1) - (y1 * x2 + y2 * x3 + y3 * x4 + y4 * x1)| / 2
Using the given coordinates, the area of the quadrilateral is:
Area = |(2 * 3 + 8 * 11 + 11 * 7 + 3 * 8) - (3 * 8 + 11 * 11 + 7 * 3 + 8 * 2)| / 2
= |(6 + 88 + 77 + 24) - (24 + 121 + 21 + 16)| / 2
= |195 - 182| / 2
= 13 / 2
= 6.5 square units
Therefore, the area of the quadrilateral is 6.5 square units.
To find the area of a quadrilateral, we can use the Shoelace formula.
1. First, write down the coordinates of the vertices in a clockwise or counterclockwise order.
(2, 3), (8, 3), (8, 11), (11, 7)
2. Multiply the x-coordinate of each vertex by the y-coordinate of the next vertex. Then, multiply the y-coordinate of each vertex by the x-coordinate of the next vertex.
(2 * 3) + (8 * 11) + (8 * 7) + (11 * 3) - ((3 * 8) + (11 * 8) + (7 * 11) + (3 * 2))
3. Add all the products from step 2 together.
6 + 88 + 56 + 33 - 24 - 88 - 77 - 6 = 8
4. Take the absolute value of the sum obtained in step 3 and divide it by 2.
Area = |8| / 2 = 4 square units
Therefore, the area of the given quadrilateral is 4 square units.