Finding the area of a Trapezoid

Area of a Trapezoid

Here is a link to the video that goes over the two trapezoid area problems.

http://www.youtube.com/watch?v=y0UWiXIaCRw

Let’s first look at where the formula for the area of a trapezoid comes from.

The formula for the area of a trapezoid  equals 1/2h(b1 + b2)  h=height

First a trapezoid has two parallel bases. If you draw a line top vertex straight down it forms a triangle.

 

 

Next, I will rotate the triangle all the way around it forms a rectangle.

 

 

 

 

The rectangle has the same area as the original trapezoid and the two bases are equal to each other and is equal to the mid segment. Now when you add the two bases together and multiply by ½ you get an average of the two bases and then multiplying this average by the height. So that is where the formula comes from it the mid segment times the height.

 

Problem 1. Find the area of a trapezoid with a height of 10 units and a base of 12 units and a base of 16 units.

 

 

 

 

Step 1.Plug in 12 and 16 for b1 and b2

  ½ 10 (12 + 16)  

 

 Step 2. ½ (10 * 28)

 

 Step 3.½(280) = 140 units

 

 Problem 2.Find the area of a trapezoid with bases of 5 and 9 and the length of the leg is 4 units. The angle measure is 60◦.

 

 

 

 

Step 1.The leg is not your height so you have to find your height.

Since you have a 60◦ angle and a 90◦ angle with the triangle you can take ½ the hypotenuse to get the short leg which equals 2 units ( In a 30,60,90 Triangle the short leg equals 1/2 the hypotenuse)

Next take the length of short leg times 2√3 = the height of the trapezoid

 

 Step 2. Plug in your number in the area formula 

½*2√3 ( 5+9)

 

 Step. 3½ * 2√3 ( 14) = ½ 28√3

 

 Step 4.14√3 = units squared equals the area of the trapezoid

 

 

Finding the area of a rhombus

Area of a Rhombus

Let’s look at a couple of problems that go over finding the area of a rhombus. A rhombus is a quadrilateral that also has the following properties,

•             A parallelogram with four congruent sides

•             Diagonals are perpendicular and bisect a pair of opposite angles

•             Diagonals are not congruent

Problem 1 Find the area of a rhombus that has a side of 12 units and a height of 10 units

Step 1. The area formula equal’s base x height. (Please note: The height is not the side but is altitude)

Step 2. Plug in your numbers 12 x 10 = 120 square units

Let’s looks at a little more challenging problem

Problem 2 Fine area of a rhombus that has diagonal that measures 10 units and the other diagonal measures 14 units.

Step 1. Use the formula for the area of a rhombus  1/2d1* d2   where d = the diagonal length

Step 2 Plug in your numbers ½ (10 *14)

            ½ *(140) = 70 units squared equals the area of the rhombus

[You tube=http://www.youtube.com/watch?v=6F3kagVBpO8]

                               

The Quadrilateral Family

The Quadrilateral Family

Four sided polygon

 

          Kite

·        A Quadrilateral that has two consecutive pairs of congruent sides

                                         But opposite sides are not congruent

·        Diagonals are not congruent

·        One pair of opposite angles that are congruent

·        The other pair of opposite angles are bisected by one of the diagonals

·        Diagonals are not congruent

 

 

Parallelogram

·        A quadrilateral with both pairs of sides parallel

·        Opposite angles and sides are congruent

·        Consecutive angles are supplementary

·        Diagonals Bisect one another

                

Trapezoid

·        A quadrilateral with exactly one pair of opposite sides parallel

·        Leg angles are supplementary

             

   

Isosceles Trapezoid

·        A trapezoid whose legs are congruent

·        Both pairs of base angles are congruent

·        Diagonals are congruent

 Rhombus

·        A parallelogram with four congruent sides

·        Diagonals are perpendicular and bisect a pair of opposite angles

·        Diagonals are not congruent

Rectangle

·        A parallelogram with four congruent 90 degree angles

·        Diagonals are congruent

·        Diagonals create four isosceles triangles

Square

·        A parallelogram with four congruent angles and sides

·        Diagonals are congruent

·        Has all the properties of a rhombus and a rectangle