## Area of rectangles

Teaser and introduction goes here. Sample problem here.

 Area is the number unit squares that fit inside a figure. A unit square is a square that is one unit long by one unit wide where the unit of length can be millimeters, inches, feet, miles, etc. To find the area of a rectangle, you need to imagine it being cut into its unit squares, and then count the number of unit squares inside that rectangle. In this 4-by-6 rectangle it is pretty easy to see that the rectangle can be cut into 24 unit squares. If each unit square is 1 cm-by-1 cm, then we say the area of the rectangle is 24 square centimeters. This is often written as 24 cm^2.

Rather than counting all the unit squares in the 4-by-6 rectangle, a quicker method for finding the number of unit squares in a rectangle is to multiply the length of the base by the height.

6 cm • 4 cm = 24 cm^2

What is the area of a rectangle with a base of 5 units and a height of 8 units? As we have already learned, you need to imagine the rectangle cut into its unit square and then counting the unit squares. A shortcut is to multiply the base by height.

Area = base • height

Area = bh

Area =(5 units)(8 units) = 40 u^2

Area of other shapes

Finding the area of other shapes is essentially the same as finding the area of a rectangle. You need to count the number of unit squares inside the figure. This is the case whether the figure is a rectangle, triangle, trapezoid, or circle.   For each figure, there is a formula for finding the number of unit squares rather than having to count the unit squares one-by-one. These formulas will be explain in other parts of this website.

 Directions: Use the "height" and "base" sliders to create a rectangle. The "Show/Hide Grid" determines whether the grid is showing. Use the slider to choose whether to display the perimeter or the area of the rectangle. • Find a formula for calculating the perimeter of the rectangle. • Find a formula for calculating the area of the rectangle.

# Self-Check

 Question 1 Find the area of this rectangle. [show answer] A = bh A = (3)(4) = $12 \,u^2$

 Question 2 Find the area of this rectangle. [show answer] A = bh A = (6)(5) = $30 \,u^2$

 Question 3 A rectangle with a base of 6 centimeters has an area of $78 \,cm^2$. What is the height of this rectangle? [show answer] A = bh 78 = 6h $h=\frac{78}{6}=13\mbox{ cm}$