FINDING AREA IN THE COORDINATE PLANE
About "Finding area in the coordinate plane"
Finding area in the coordinate plane :
We can use familiar area formulas to find areas of polygons in the coordinate plane.
Finding area in the coordinate plane - Examples
Example 1 :
A gardener uses a coordinate grid to design a new garden. The gardener uses polygon WXYZ on the grid to represent the garden. The vertices of this polygon are W(3, 3), X(−3, 3), Y(−3, −3), and Z(3, −3). Each grid unit represents one yard.Find the area of the garden.
Solution :
Step 1 :
Graph the vertices, and connect them in order.
From the graph, it clear that the shape of the garden is a square.
Let us find lengths of the sides YZ and WZ.
Step 2 :
Find the length of the side YZ.
The ordered pair of Y is (-3, -3).
The x-coordinate of Y is -3, so point Y is |-3| = 3 yards from the y-axis.
The ordered pair of Z is (3, -3).
The x-coordinate of Z is 3, so point Z is |3| = 3 yards from the y-axis.
Find the sum of the distances :
The length of side YZ = 3 + 3 = 6 yards
Step 3 :
Find the length of the side WZ.
The ordered pair of W is (3, 3).
The y-coordinate of W is 3, so point W is |3| = 3 yards from the x-axis.
The ordered pair of Z is (3, -3).
The y-coordinate of Z is -3, so point Z is |3| = 3 yards from the x-axis.
Find the sum of the distances :
The length of side WZ = 3 + 3 = 6 yards.
Step 4 :
Find the area of the square WXYZ using the lengths of the sides YZ and WZ.
Area of the square WXYZ = side x side
Area of the square WXYZ = YZ x WZ
Area of the square WXYZ = 6 x 6
Area of the square WXYZ = 36 square yards.
Example 2 :
Caleb is planning a new deck for his house. He graphs the deck as polygon ABCDEF on a coordinate plane in which each grid unit represents one foot. The vertices of the polygon are A(1, 0), B(3, 2), C(3, 5), D(8, 5), E(8, 2), and F(6, 0). What is the area of Caleb’s deck ?
Solution :
Step 1 :
Graph the vertices, and connect them in order.
Draw a horizontal dashed line segment to divide the polygon into two quadrilaterals — a rectangle and a parallelogram.
Step 2 :
Find the area of the rectangle using the length of segment BE as the base b and the length of segment BC as the height h.
b = |8| − |3| = 5 feet
h = |5| − |2| = 3 feet
A = bh = 5 x 3 = 15 square feet
Step 3 :
Find the area of the parallelogram using the length of segment AF as the base. Use the length of a segment from F(6, 0) to the point (6, 2) as the height h.
b = |6| − |1| = 5 feet
h = |2| − 0 = 2 feet
A = bh = 5 x 2 = 10 square feet
Step 4 :
Add the areas to find the total area of the deck.
hence, the required area is
= 15 + 10 = 25 square feet
After having gone through the stuff given above, we hope that the students would have understood "Finding area in the coordinate plane".
Apart from the stuff given above, if you want to know more about "Finding area in the coordinate plane", Please click here
Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.
You can also visit our following web pages on different stuff in math.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Time and work word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Recent Articles
-
Formula for a Squared minus b Square
Aug 17, 19 07:24 AM
Formula for a Squared minus b Square - Example Problems and Step by Step Solutions
-
Formula for a plus b Whole Square
Aug 17, 19 06:39 AM
Formula for a plus b Whole Square - Example Problems and Step by Step Solutions
-
Formula for a minus b Whole Square
Aug 17, 19 06:35 AM
Formula for a minus b Whole Square - Example Problems and Step by Step Solutions
