THE trapeze area measures the surface value of this flat figure formed by four sides.
The trapeze is a quadrilateral that has two sides and two parallel bases, one larger and one smaller.
The trapeze is considered a remarkable quadrilateral, so the sum of its internal angles corresponds to 360°.
Trapeze Classification
Trapezies are classified into three types:
- Rectangle Trapeze: presents two 90º angles, called right angles.
- Isosceles or Symmetrical Trapezium: non-parallel sides are congruent (have the same measurement).
- Scalene Trapeze: all sides have different measurements.
Area formula
To calculate the trapeze area we use the following formula:
Where:
THE: figure area
B: larger base
B: smaller base
H: height
Perimeter formula
To calculate the perimeter of the trapeze, the formula is used:
P = B + b + L_{1} + L_{2}
Where:
P: perimeter (sum of all sides)
B: larger base
B: smaller base
L_{1 }and L_{2: }sides of the figure
Learn more about the topic in the articles:
- trapeze
- plane geometry
- Area and Perimeter
- Polygon Area
- Perimeters of Flat Figures
- Flat Figure Areas
- Flat Figures Area - Exercises
Solved Exercises
1. Calculate the area of a trapeze with a height of 5 cm and bases of 8 cm and 3 cm.
B: 8cm
b: 3 cm
h: 5 cm
To calculate your area, just replace the values in the formula:
A = 8+3/2. 5
A = 11/2. 5
A = 5.5. 5
H = 27.5 cm^{2}
2. Determine the measurement of the smallest base of a 100 cm trapezoid^{2} of area, 10 cm in height and base greater than 15 cm.
H: 100 cm^{2}
h: 10 cm
B: 15 cm
By substituting the values in the formula, we can find the lowest base value:
100 = 15 + b/2. 10
100 = 15 + b. 5
100/5 = 15 + b
20 -15 = b
b = 5 cm
To check if the value found is correct, substitute in the formula:
A = 15 + 5/2 .10
A = 20/2. 10
A = 20.5
H = 100 cm^{2}
3. How tall is a trapeze with an area of 50 cm^{2}, base larger than 6 cm and smaller than 4 cm?
H = 50 cm^{2}
B = 6 cm
b = 4 cm
50 = 6 + 4/2. H
50 = 10/2. H
50 = 5h
h = 50/5
h = 10 cm
Once the value is found, check if it is correct, using the formula again:
A = 6 + 4/2. 10
A = 10/2. 10
A = 5. 10
H = 50 cm^{2}
How about finding out more about the areas of other flat figures?
- Circle Area
- Triangle Area
- Diamond Area
- Square Area
- Rectangle Area
- Parallelogram Area
- Math Formulas