The Trapezoid Has Two Bases That Are of Different Lengths
File: Area of Rectangles: Example 1
Area of Rectangles: Example 1
Determine the area of a rectangle measuring 4’ by 36”.
Possible Solution:
Step 1: / draw and label a diagram
Step 2: / convert both measurements to the same unit (either feet or inches)
4’ = 4 x 12” or 48”
Step 3: / use the formula A = bh to determine the area
Step 4: / state the answer in a complete sentence
The sandbox will cover 1728 in2 of the yard.
For an alternate solution, click here.
Click here:
File: Area of Rectangles: Example 2
Area of Rectangles: Example 2
The store has a carpet remnant that has an area of 36 ft2, and it is 4’ wide. How long is this piece of carpet?
Possible Solution
Step 1: / draw and label a diagram
Step 2: / select the formula that relates the area of a rectangle to its base
Step 3: / substitute the known values into the formula and solve for the unknown dimension
Step 4: / state the answer in a complete sentence
The carpet is 9 feet in length.
File: Area of Triangles
Area of Triangles
A triangle is half of a rectangle. Take any rectangle, and fold it along its diagonal line. The result is two equal triangles.
If the formula for the area of a rectangle is A = bh, then it makes sense that the formula for the area of a triangle is half of that, or .
Again, we must always remember that the height is perpendicular to the base.
Example 1: Determine the area of the following triangle:
Possible Solution:
Step 1: / write down the formula for the area of a triangle
Step 2: / substitute the known values into the formula and determine the area
Step 3: / state the answer in a complete sentence
The area of the triangle is 30 cm2.
File: Area of Triangles: Example 2
Area of Triangles: Example 2
If the area of a triangle is 45 cm2, and the base is 9 cm, determine its height.
Possible Solution:
Step 1: / draw and label a diagram
Step 2: / select the formula that relates the area of a triangle to its base
Step 3: / substitute the known values into the formula and solve for the height
Step 4: / state the answer in a sentence
The height of the triangle is 10 cm.
To see another area of a triangle example, click here:: Example 3
File: Parallelograms
Parallelograms
A parallelogram does not usually have right-angle corners. The opposite sides are parallel with each other, and are the same length.
To calculate the area of a parallelogram, we need to determine the height of the parallelogram. The height will meet the base at a right angle.
Example:
Given //gm ABCD, determine its area.
Note that “//gm” is an abbreviation for parallelogram. Because ABCD is a //gm, we know that its opposite sides are the same length and parallel.
Possible Solution:
Step 1: / select the appropriate formula
Step 2: / substitute the known values into the formula and determine the area
Step 3: / state the answer in a sentence
The area of //gram ABCD is 60 square inches.
File: Trapezoids
Trapezoids
Trapezoids are very interesting shapes. They have at least one set of parallel sides that are different lengths.
- The trapezoid has two bases that are of different lengths.
- Also notice the height meets the base at a right angle.
- The formula for finding area of a trapezoid is as follows:
Note that the formula uses the average length of the two bases:
File: Trapezoids: Example
Trapezoids: Example
Given the following trapezoid, calculate the area.
Possible Solution
Notice that the height (6 cm) meets one of the bases at a right angle.
Step 1: / select the appropriate formula
Step 2: / substitute the known values into the formula and determine the area
Step 3: / state the answer in a sentence
The area of the trapezoid is 58.8 cm2
File: Reflect On Your Learning
Reflect On Your Learning
Key Ideas
- Different formulas are used to calculate the area of various shapes.
- The area of a figure is always expressed in square units: cm2, ft. 2, m2, etc.
- The base-height relationship is common to many area formulas. The height of a figure is measured perpendicular to its base.
- when solving problems involving area calculations, it’s always a good idea to draw a diagram of the shape, and label all the parts that you know the measures for.
- In all situations using formulas to calculate area, you must be sure that all the units of measurement are the same.
File: Perimeter and Area: Example 1
Perimeter and Area: Example 1
We can use diagrams drawn to scale to find actual perimeter and area.
This is a drawing of a garden in your yard. Note the scale on the drawing.
Use that scale to determine the actual perimeter and area of the garden.
Possible Solution
- Since 1 cm represents 1 m, then 4.2 cm represents 4.2 m, and 9.4 cm represents 9.4 m.
- So the actual dimensions of the garden are 4.2 m x 9.4 m.
- The perimeter of the garden is:
- The area of the garden is:
File: Perimeter and Area: Example 2
Perimeter and Area: Example 2
This trapezoid has a scale of 1 cm: 9 cm.
- Calculate the perimeter of this figure.
- Calculate the area of this figure.
Step 1: / Sometimes it’s a good idea to re-label your diagram with the actual measurements.
Step 2: / Calculate the perimeter.
Note, because the bases are of different length, just add up the sides.
Perimeter = 54 cm + 45 cm + 90 cm + 45 cm
Perimeter = 234 cm
Step 3: / Calculate the area.
Want to see how to convert this area to square metres? Click here: