how to find the area of trapezoid
Surface area of Trapezoid
The area of a trapezoid is the number of unit squares that can be fit into it and it is measured in square units (like cm2, m2, in2, etc). For example, if fifteen unit squares each of length ane cm can exist fit inside a trapezoid, then its surface area is xv cm2. A trapezoid is a type of quadrilateral with one pair of parallel sides (which are known equally bases). It ways the other pair of sides can be not-parallel (which are known as legs). It is not e'er possible to describe unit squares and measure the area of a trapezoid. So, let us acquire about the formula to find the area of a trapezoid on this page.
| one. | What is the Area of Trapezoid? |
| 2. | Expanse of Trapezoid Formula |
| 3. | Surface area of Trapezoid without Height |
| iv. | How to Derive Area of Trapezoid Formula? |
| 5. | Area of Trapezoid Calculator |
| 6. | FAQs on Area of Trapezoid |
What is the Area of Trapezoid?
The area of a trapezoid is the total infinite covered by its sides. An interesting point to exist noted here is that if we know the length of all the sides we can simply split the trapezoid into smaller polygons similar triangles and rectangles, find their area, and add together them upward to get the area of the trapezoid. However, there is a straight formula that is used to notice the area of a trapezoid if we know certain dimensions.
Surface area of Trapezoid Formula
The surface area of a trapezoid tin be calculated if the length of its parallel sides and the altitude (height) between them is given. The formula for the area of a trapezoid is expressed equally,
A = ½ (a + b) h
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the peak (the perpendicular distance betwixt a and b)
Example:
Find the expanse of a trapezoid whose parallel sides are 32 cm and 12 cm, respectively, and whose height is v cm.
Solution:
The bases are given as, a = 32 cm; b = 12 cm; the pinnacle is h = 5 cm.
The expanse of the trapezoid = A = ½ (a + b) h
A = ½ (32 + 12) × (5) = ½ (44) × (5) = 110 cm2.
Surface area of Trapezoid without Peak
When all the sides of the trapezoid are known, and we do not know the height nosotros tin discover the area of the trapezoid. In this case, we first need to calculate the summit of the trapezoid. Let united states of america understand this with the help of an instance.
Example: Detect the area of a trapezoid in which the bases (parallel sides) are given as vi and fourteen units respectively, and the non-parallel sides (legs) are given equally, 5 units each.
Solution: Allow us calculate the area of the trapezoid using the following steps.
- Step 1: We know that the area of a trapezoid = ½ (a + b) h; where h = height of the trapezoid which is not given in this case; a = 6 units, b = 14 units, non parallel sides (legs) = v units each.
- Step 2: So, if nosotros find the top of the trapezoid, nosotros can calculate the expanse. If nosotros depict the superlative of the trapezoid on both sides we can see that the trapezoid is split into a rectangle ABQP and 2 right-angled triangles, ADP and BQC.
- Step iii: Since a rectangle has equal opposite sides, this means AP = BQ and it is given that the sides AD = BC = v units. So, the top AP and BQ can be calculated using the Pythagoras theorem.
- Step 4: At present, let united states of america find the length of DP and QC. Since ABQP is a rectangle, AB = PQ and DC = 14 units. This means PQ = 6 units, and the remaining combined length of DP + QC tin be calculated as follows. DC - PQ = fourteen - 6 = 8. So, eight ÷ 2 = four units. Therefore, DP = QC = 4 units.
- Step 5: Now, the peak of the trapezoid tin exist calculated using the Pythagoras theorem. Taking the right-angled triangle ADP, nosotros know that AD = five units, DP = four units, so AP = √(Advertising2 - DPii) = √(fiveii - 42) = √(25 - 16) = √9 = iii units. Since ABQP is a rectangle, in which the opposite sides are equal, AP = BQ = 3 units.
- Stride half-dozen: At present, that we know all the dimensions of the trapezoid including the superlative, nosotros tin can summate its expanse using the formula, area of a trapezoid = ½ (a + b) h; where h = 3 units, a = 6 units, b = 14 units. After substituting the values in the formula, we get, area of a trapezoid = ½ (a + b) h = ½ (half-dozen + 14) × iii = ½ × xx × 3 = 30 unitii.
How to Derive Expanse of Trapezoid Formula?
We can evidence the area of a trapezoid formula by using a triangle hither. Taking a trapezoid of bases 'a' and 'b' and height 'h', allow united states of america prove the formula.
- Step 1: Split one of the legs into two equal parts and cut a triangular portion of the trapezoid as shown.
- Step 3: Attach information technology at the bottom as shown, such that it forms a big triangle.
- Step 4: This mode, the trapezoid is rearranged every bit a triangle. Even later we attach it this fashion, we know that the area of the trapezoid and the new big triangle remains the same. Nosotros can also see that the base of the new big triangle is (a + b) and the height of the triangle is h.
- Step 5: Then, it can be said that the area of the trapezoid = the area of the triangle
- Pace 6: This can be written as, area of the trapezoid = ½ × base of operations × meridian = ½ (a + b) h
Thus, we have proved the formula for finding the expanse of a trapezoid.
Expanse of Trapezoid Estimator
The expanse of a trapezoid is the number of unit of measurement squares that tin fit into it. Area of trapezoid calculator is an online tool that helps to notice the area of a trapezoid. If sure parameters such as the value of base of operations or meridian is available nosotros can directly give the inputs and calculate the area. Try Cuemath's Area of a Trapezoid Figurer and calculate the area of a trapezoid within a few seconds. For more practice cheque out the area of trapezoid worksheets and solve the problems with the help of the calculator.
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Area of Trapezoid Examples
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Example two: Find the area of an isosceles trapezoid in which the length of each leg is 8 units and the bases are equal to 13 units and 17 units respectively.
Solution:
The bases are a = 13 units and b = 17 units. Permit united states assume that its height is h.
We can divide the given trapezoid into two congruent right triangles and a rectangle every bit follows:
From the above effigy,
x + x + 13 = 17
2x + 13 = 17
2x = 4
x = 2
Using Pythagoras theorem,
x2 + h2 = 82
22 + h2 = 64
4 + hii = 64
h2 = 60
h = √sixty = √4 × √15 = ii√15
The area of the given trapezoid is,
A = ½ (a + b) h
A = ½ (13 + 17) × (2√15) = 30√15 = 116.eighteen foursquare units
Answer: The expanse of the given trapezoid = 116.eighteen square units.
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Practice Questions on Area of Trapezoid
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FAQs on Area of Trapezoid
What is Area of Trapezoid in Math?
The surface area of a trapezoid is the number of unit of measurement squares that tin fit into information technology. Nosotros know that a trapezoid is a four-sided quadrilateral in which one pair of opposite sides are parallel. The area of a trapezoid is calculated with the aid of the formula, Surface area of trapezoid = ½ (a + b) h, where 'a' and 'b' are the bases (parallel sides) and 'h' is the perpendicular height. It is represented in terms of square units.
How to Find the Area of a Trapezoid?
The area of a trapezoid is plant using the formula, A = ½ (a + b) h, where 'a' and 'b' are the bases (parallel sides) and 'h' is the height (the perpendicular distance between the bases) of the trapezoid.
Why is the Surface area of a Trapezoid ½ (a + b) h?
The formula for the expanse of a trapezoid can exist proved hands. Consider a trapezoid of bases 'a' and 'b', and elevation 'h'. We can cutting a triangular-shaped portion from the trapezoid and adhere information technology at the bottom then that the unabridged trapezoid is rearranged every bit a triangle. Then the triangle obtained has the base (a + b) and height h. By applying the expanse of a triangle formula, the expanse of the trapezoid (or triangle) = ½ (a + b) h. For more data, you can refer to How to Derive Area of Trapezoid Formula? section of this page.
How to Discover the Missing Base of a Trapezoid if you Know the Area?
Nosotros know that the area of a trapezoid whose bases are 'a' and 'b' and whose height is 'h' is A = ½ (a + b) h. If one of the bases (say 'a'), height, and expanse are given, then we will but substitute these values in the above formula and solve it for the missing base (a) as follows:
A = ½ (a + b) h
Multiplying both sides by ii,
2A = (a + b) h
Dividing both sides by h,
2A/h = a + b
Subtracting b from both sides,
a = (2A/h) - b
How to Find the Height of a Trapezoid With the Area and Bases?
If the area and the bases of a trapezoid is known, then we can calculate its height using the formula, Area of trapezoid = ½ (a + b) h; where 'a' and 'b' are the bases and 'h' is the height. In other words, we can find the height of the trapezoid by substituting the given values of the area and the 2 bases.
How to Find the Area of an Isosceles Trapezoid Without the Height?
If the height of the trapezoid is not given and all its sides are given, and then nosotros tin can split up the trapezoid into two congruent right triangles and a rectangle. Using the Pythagoras theorem in the right-angled triangles, we can calculate the height. Afterwards we go the elevation, we can use the formula, A = ½ (a + b) h, to get the area of the trapezoid.
What is the Formula for Area of Trapezoid?
The formula that is used to find the area of a trapezoid is expressed as, Area of trapezoid = ½ (a + b) h; where a' and 'b' are the bases (parallel sides) and 'h' is the meridian of the trapezoid.
Source: https://www.cuemath.com/measurement/area-of-trapezoid/
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