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

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

Step 1. Plug in 12 and 16 for b1 and b2 and 10 for the height. 
             ½ 10 (12 + 16)  

Step 2. ½ (10 * 28)

Step 3. ½(280) = 140 units squared

Problem 2. Find the trapezoid area, 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. ( In a 30-60-90 Triangle the short leg equals 1/2 the hypotenuse)
Short leg =1/2 x 4 = 2 units

Step 2 Now you can find the height by taking the short leg x √3 
            2√3 = Height 
Step 3 Plug in your number in the area formula  1/2h (b1 + b2)
             ½*2√3 ( 5+9)

Step 4  ½ * 2√3 ( 14) = ½ 28√3

Step 5 14√3 = units squared equals the area of the trapezoid

The hypotenuse is always opposite the right angle 


Area of a Trapezoid

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6th Grade Math-Area of a Rhombus

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

Step 1. Formula for area of a Rhombus equals  base x height. (Please note: The height is not the side but is the altitude) 

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

Let’s looks at a little more challenging problem

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

Step 1. Use the formula 1/2d* d2   d = the diagonal length

Step 2. Plug in your numbers ½ (10 *14) 
              ½ *(140) = 70 units squared equals the area of the rhombus

What are plane shapes? Plane shapes are polygons in two dimensions. A polygon is a two dimensional shape that has straight lines that join to form a closed figure. The straight lines or segments ( also called sides) join at endpoints called vertices. The more common plane shapes are, squares,rectangles,parallelograms,rhombuses,trapezoids,and triangles.
How do you find the area of these shapes? Once you know the formula for each shape you just plug in the appropriate numbers. Let's look at some example problems for finding the area of plane shapes and then a video for each plane shape.

Rhombus Area and Trapezoid Area

trapezoid 4x5x4x9
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pizza shape
Step by step instructions for finding the area of a trapezoid
Step by step instructions for finding the area of a rhombus
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​The short leg is 1/2 the hypotenuse
1/2 x4=2 units
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Common Core Standard: 6.G.1  6th Grade Math