Quick Math Homework Help
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Common Core Standard  7.G.6    7th grade Math
(1,2).
(4,2).
(1,0).
(4,0).

### Area of a rectangle vertices

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.

When you draw the rectangle on a coordinate plane and count the number of squares you get 6 unit^2
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?
Hypotenuse
Leg
Leg
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 the area of a rectangle.

​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^2=144

b=√144
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.

The area of a rectangle equals the amount of space found inside the boundary of this (2-dimensional) shape. The formula used to find the area of a rectangle equals, (base of the rectangle x-height of the rectangle). Is the area of a rectangle the same as perimeter? Now think of a football field enclosed by a fence. The length of the fence that surrounds the field would be your perimeter, and the amount of space inside the fence is the area. Because the area of a rectangle is calculated with base and height, it is a 2-dimensional measure and is expressed in square units. (units^2) In a rectangle the opposite sides are congruent, so if you know the measure of one side of the rectangle then it will equal the measure of the opposite side. This information is useful when trying to find the area of a rectangle.