how to find the area of a trapezium
Area of Trapezium
The surface area of a trapezium is defined as the number of unit of measurement squares that can fit into information technology and information technology is measured in square units (like cm2, m2, inii, etc). A trapezium is a type of quadrilateral that has one pair of parallel sides(mostly referred to as bases). The other pair of sides of a trapezium tin can be non-parallel and are known equally legs. The expanse of a trapezium is the total space covered by a trapezium in a two-dimensional aeroplane. For example, if 20 unit of measurement squares each of length 1 in tin can be fit inside a trapezium, and then its area is 20 in2. It is not always possible to draw unit squares and hence mensurate the area of a trapezium. Nosotros volition acquire near the area of a trapezium and the formula to summate information technology on this page.
| i. | Area of Trapezium Formula |
| 2. | How to Derive Area of Trapezium Formula? |
| 3. | How To Calculate Surface area of Trapezium? |
| iv. | FAQs on Area of Trapezium |
Area of Trapezium Formula
The surface area of a trapezium can be calculated using the lengths of ii of its parallel sides and the distance (height) between them. The formula to calculate the area (A) of a trapezium using base and superlative is given as,
A = ½ (a + b) h where,
- a and b = bases of trapezium, and,
- h = height (the perpendicular altitude between a and b)
How to Derive Area of Trapezium Formula?
We tin can derive the formula to find the surface area of a trapezium in two ways:
- Using a parallelogram
- Using a triangle
Derivation of Expanse of Trapezium Formula Using a Parallelogram
To derive the formula for the area of a trapezium using parallelogram, we volition consider ii identical trapeziums, each with bases a and b and elevation h. Allow A exist the area of each trapezium. Assume that the second trapezium is turned upside down as shown in the effigy below.
At present, bring together the above 2 trapeziums.
Nosotros can see that the new figure obtained past joining the two trapeziums is a parallelogram whose base is a + b and whose height is h. We know that the surface area of a parallelogram is base × height. The area of the above parallelogram is, A + A = 2A.
Thus, 2A = (a + b) h
⇒ A = (a+b)h/ii
Thus, the formula for the area of a trapezium is derived.
Derivation of Area of Trapezium Formula Using a Triangle
We volition derive the area of a trapezium formula by using a triangle hither. Consider the higher up trapezium of bases a and b and peak h. In order to derive the formula,
- Pace 1: Dissever one of the legs of the trapezium into ii equal parts.
- Step 2: Cutting a triangular portion from the trapezium (as shown in the superlative figure of the below diagram).
- Pace 3: Attach information technology at the bottom (as shown in the bottom effigy in the diagram below).
The trapezium tin can thus be rearranged as a triangle. It can exist concluded from the in a higher place diagram that the areas of both the trapezium and the triangle are equal. Also, it can exist observed that the base of the triangle is equal to (a + b) and the height of the triangle is h.
The surface area of the trapezium = The area of the triangle = ½ × base × height = ½ (a + b) h
How To Calculate Area of Trapezium?
The steps given below can be followed to find the area of a trapezium:
- Step 1: Annotation the dimensions of the lengths of the parallel sides (bases) of the trapezium from the given data.
- Footstep 2: Calculate the sum of the bases.
- Step 3: Multiply the value of the sum of bases past acme or altitude of the trapezium and past 1/2.
- Step iv: Write the answer in square units.
Surface area of Trapezium Examples
-
Case two: Find the area of an isosceles trapezium with the length of each leg to be xiii units and the bases are of lengths 22 units and 12 units.
Solution:
Given:
Bases, b = 22 units; a = 12 units.
Let us assume that its top to be h. Nosotros tin split up the given trapezium into two congruent right triangles and a rectangle as follows:
From the above effigy,
x + x + 12 = 22
⇒ 2x + 12 = 22
⇒ 2x = 10
⇒ x = five
Using Pythagoras theorem,
x2 + h2 = thirteenii
⇒ 52 + htwo = 169
⇒ 25 + h2 = 169
⇒ h2 = 144
⇒ h = √144 = 12
The area of the given trapezium is,
A = ½ (a + b) h
⇒ A = ½ (12 + 22) (12) = 204 square units
Answer: The area of the given trapezium = 204 square units.
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Practice Questions on Area of Trapezium
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FAQs on Area of Trapezium
What is the Surface area of a Trapezium?
The area of a trapezium is the total space covered past the shape in the 2-dimensional plane. To calculate the area of a trapezium, we just multiply the sum of bases with the elevation and divide the obtained product by two.
How to Notice the Area of Trapezium Without Height?
If the height of the trapezium is not given and all its sides are given instead, and so nosotros will split up it into 2 correct triangles and a rectangle. The areas of each of these shapes tin be calculated and added to observe the expanse of the given trapezium.
How to Calculate Area of Trapezium Using Base of operations and Top?
The area of a trapezium, given the height and bases, can exist calculated by multiplying the average of the base lengths with the height of the trapezium. The acme of a trapezium is simply the altitude between the parallel sides.
What are the Formulas for Perimeter and Area of Trapezium?
The area of a trapezium can be calculated using the formula: A = ½ × (a + b) × h. While the formula to calculate the perimeter of the trapezium is given as: P = a + b + c + d.
where,
- a, b, c, and d = Length of sides of a trapezium
- h = Altitude between the two parallel sides i.e., a and b.
How practise you Prove the Area of a Trapezium Formula?
The area of a trapezium formula tin exist proved by rearranging the trapezium in form of a parallelogram or a triangle. The area of the shapes thus obtained can exist related to a trapezium for proving the area of a trapezium formula.
What is the Use of Area of Trapezium Computer?
Surface area of trapezium calculator is used to calculate the area of trapezium by entering the given specific parameters. Such as height and the value of the bases. It gives the measurement easily and rapidly. Endeavour Cuemath's surface area of trapezium calculator and get your answers but by a click.
How practise you lot Find the Surface area of a Trapezium Using Sides?
The area of a trapezium tin be calculated if the measurements of its sides are known. For this, we can divide the shape in the form of a rectangle and ii right-angled triangles. The peak can be calculated applying Pythagoras theorem in one of the right-angled triangles and finally, we can apply the area of the trapezium formula to summate the required area.
Source: https://www.cuemath.com/measurement/area-of-trapezium/
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