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Common Core Standard  7.G.6    7th grade Math
coordinate plane
Quick review of a rectangle

  • A Rectangle is a four sided polygon
  • The opposite sides are congruent
  • The sides that are opposite are parallel
  • A rectangle has four right angles

For more on a Rectangle see: What is a rectangle?
pythagorean theorem
Quick Review of the Pythagorean Theorem

The Pythagorean Theorem is used with right triangles in order to find missing sides. It states that the sum of the square of the two legs is equal to the hypotenuse squared. It is written as follows:

How to find area of a rectangle with diagonal.

How to find the area of a rectangle.

rectangle 8x10/How to find the area of a rectangle
horizontal line
horizontal line

Area of a Rectangle formula equals b x h (base x height )

How to find the area of a rectangle.

rectangle with diagonal of 15 units/how to find the area of a rectangle
area formulas plane shape
what is a plane shape
area of circles
​Step 1. Plug the numbers into the formula b*h 

8 * 10 =80 units squared

Next, let’s look at a more challenging problem. 
Problem 2. Find the base of a rectangle with an area of 100 units and a height of 5 units.

Step 1. Write the formula for the area of a rectangle Area= b*h

Step 2. Plug in what you know 100 = b * 5

Step 3 Divide each side by 5 
  100/5= b/5  
Problem 3. Find the area of a rectangle with a diagonal of 15 units and a side of 9 units.

Step 1. Plug in what you know A = b * 9

Step 2. The diagonal divides the rectangle into a right triangle. You can use the Pythagorean Theorem to find the base. 

A = 9 c= 15 b=your unknown (see picture below)
9^2+ b^2= 15^2 

81+ b^2=225


b = 12

Step 3 Use your area formula of a rectangle  
            Area = b*h
​Step 4. 20 =b and b = the base of the rectangle
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Find the area of a rectangle with a base of 10 units and a height of 8 units.

One can easily calculate the area of a rectangle from the vertices of a rectangle. The vertices are the points where two or more straight lines meet. The base and height of the rectangle is the difference between the values of the vertices. 

For example: What is the area of a rectangle with the following coordinates, (1,2)(1,0) (4,2)(4,0)
The base and height are just the difference between these values.
Base = 4-1=3, Height = 2-0= 2
Next, multiply the base and the height = 3*2=6 unit^2 is the area

Another method is to plot the points on a coordinate plane and count the number of squares.