Discover the formula for finding the area of a square trapezoid when all 4 side lengths are known.

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Methods for calculating the area of a trapezoid: balanced, square, regular, uniform

Calculating the area of a trapezoid: square, balanced, when knowing the length of 4 sides, the formula

1. Method for finding the area of a trapezoid

2. How to Calculate the Area of a Right Trapezoid

3. How to Calculate the Area of an Isosceles Trapezoid

4. How to Calculate the Area of a Trapezoid when Knowing 4 Sides.

5. Exercises Related to Trapezoid Area

Trapezoids are quite common shapes in our lives, often encountered during our school days. While finding the perimeter of a trapezoid might be simple by adding up its 4 sides, remembering the formula for its area calculation can be tricky over time. In this article, Mytour will guide you on calculating the area of a square trapezoid when all 4 side lengths are known.

Although trapezoids and rectangles share many similarities, their methods of calculating area differ. Following our previous guide on calculating the area of a rectangle, today Mytour shares with you the method of calculating the area of a square trapezoid when all 4 side lengths are known. Stay tuned and share if you or someone you know needs it.

Methods for calculating the area of a trapezoid: balanced, square, regular, uniform

A trapezoid is a quadrilateral with two parallel sides. To learn more about this shape, you can check out the Wikipedia article on trapezoids.

Calculating the area of a trapezoid: square, balanced, when knowing the length of 4 sides, the formula

Article Contents:
1. Finding the area of a trapezoid.
2. Finding the area of a square trapezoid.
3. Finding the area of a balanced trapezoid.
4. Finding the area of a trapezoid when all 4 sides are known.
5. Exercises.

1. Method for finding the area of a trapezoid

To calculate the area of a trapezoid, we use the formula Height multiplied by the average of the two bases.

S = h x (a + b)1/2

Where

a: Base 1.
b: Base 2.
h: Height dropped from base a to b or vice versa (distance between the two bases).

In addition to reviewing formulas and practicing exercises, you can memorize the following poem to quickly remember the trapezoid area formula and apply it to exercises:

To find the area of a trapezoid
Add the length of the top and bottom sides together

Multiply by the height
Divide the result by 2, and there you have it!

For example, let's say we have trapezoid ABCD with side AB = 8, side CD = 13, and a height of 7 between the two bases. Then, we can calculate the area of the trapezoid as:

S_ABCD = 7 x (8 + 13)/2 = 73.5.

Similarly, for the case of a right trapezoid with height AC = 8, side AB = 10.9, side CD = 13, we calculate as follows:

S_ABCD = AC x (AB + CD)/2 = 8 x (10.9 + 13)/2 = 95.6.

2. How to Calculate the Area of a Right Trapezoid

A right trapezoid is a trapezoid with one angle equal to 90 degrees. The side perpendicular to the two bases is called the height 'h' in the trapezoid. The formula to calculate the area of a right trapezoid is similar to that of a regular trapezoid, but the height here is the side perpendicular to the two bases.

Where:

S: the area of the trapezoid.
a and b: the lengths of the two bases.
h: the height of the trapezoid (the length of the side perpendicular to the two bases).

3. How to Calculate the Area of an Isosceles Trapezoid

An isosceles trapezoid is a trapezoid with two equal sides, and the angles adjacent to one base are equal.

You can apply the formula for calculating the area of a regular trapezoid or divide the trapezoid into smaller shapes and then add them together to find the area of an isosceles trapezoid:

For example: Given isosceles trapezoid ABCD, where AD = BC and angle ADC = angle BCD. Find the area of isosceles trapezoid ABCD.

Solution: We draw the altitudes AH and BK, which intersect DC at H and K, respectively. Now, we have rectangle ABKH and two right triangles ADH and BCK.

Considering triangles ADH and BCK, we have:

AD = BC
Angle ADC = Angle BCD
Angle H = Angle K = 90 degrees
Therefore, Triangle ADH = Triangle BCK

4. How to Calculate the Area of a Trapezoid when Knowing 4 Sides.

In reality, if the problem asks how to calculate the area of a trapezoid when knowing all 4 sides, there won't be an exact answer because knowing only the 4 sides can lead to various cases and different areas. You can imagine, for example, a trapezoid with sides 4, 5, 6, 9, which can form 3 different trapezoids with different areas.

However, if the problem provides additional information, such as calculating the area of a trapezoid when knowing the lengths of all 4 sides and specifying which side is the base, then it's possible to calculate the area of the trapezoid.

For example, let's consider the bases QP, where base P is longer, and the two sides are R and S.

We apply the trapezoid area formula as follows:

Exercise 1: Given trapezoid ABCD with side AB = 5cm, side CD = 9cm, and the height between the two bases is 6cm. Calculate the area of trapezoid ABCD.
Solution:
Applying the trapezoid area formula, we have:
S_ABCD = 6 . (5 + 9) : 2 = 42 (cm²).

Exercise 2: There is a trapezoidal piece of land with a small base of 24m and a large base of 30m. Extending both bases to the right of the land piece by 7m for the large base and 5m for the small base results in a new trapezoidal land piece with an area greater than the initial area by 36m². Calculate the area of the original trapezoidal land piece.
Solution:
According to the problem, the additional area is the area of a trapezoid with a large base of 7m and a small base of 5m. Therefore, the height of the trapezoidal land piece is: h = (36 x 2) : (7 + 5) = 6 m
The area of the original land piece is: S = 6 . (24 + 30) : 2 = 162 m².

Exercise 3: Given a right trapezoid with a distance between the two bases of 16cm, where the small base is ¾ of the large base. Calculate the lengths of the two bases knowing the area of the right trapezoid is 112cm².

Solution:

The distance between the two bases in the right trapezoid is the height of the trapezoid, so:

The total length of the two bases is (112 x 2) : 16 = 14 (cm).
Let's denote the length of the small base as 'a' and the length of the large base as 'b', we have:
a + b = 14 and a = ¾ b.
Substituting, we get ¾ b + b = 14.
So, b = 14 : 7 x 4 = 8 (cm).
=> a = 14 - 8 = 6 (cm)
Therefore, the small base is 6cm, and the large base is 8cm.

Additionally, in the case of calculating the area of a trapezoid when knowing the sides, you can divide it into 2 triangles and 1 rectangle, or draw an additional line between the two lateral sides and apply the Heron's formula to calculate the area of the triangle, from which you can deduce the area of the trapezoid.

So above, Mytour has shared and reiterated to readers the previously known knowledge about calculating the area of an isosceles right trapezoid when knowing the lengths of all 4 sides. Wishing you all happiness.

In case you need to calculate the length of a rectangle when knowing the area and perimeter, you can refer to how to calculate the length of a rectangle when knowing the area and the perimeter here.

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Frequently Asked Questions

What is the formula for calculating the area of a trapezoid?

The area of a trapezoid is calculated using the formula S = h x (a + b)/2, where 'h' is the height, 'a' is one base, and 'b' is the other base. This method is effective for determining the area based on the trapezoid's dimensions.

How can I calculate the area of a square trapezoid with known sides?

To find the area of a square trapezoid when all four side lengths are known, you can use various methods, such as dividing it into triangles or applying the general trapezoid area formula, depending on the trapezoid's characteristics.

What are the characteristics of a right trapezoid in area calculation?

A right trapezoid features one right angle, with the height being the length of the side perpendicular to the two bases. The area calculation follows the same formula as a regular trapezoid, ensuring accuracy in determining the area.

Can you explain how to calculate the area of an isosceles trapezoid?

To calculate the area of an isosceles trapezoid, you can use the standard trapezoid area formula or break it down into simpler shapes like triangles and rectangles. This approach helps in finding the area accurately based on the sides.

What should I do if I know all four sides of a trapezoid?

When knowing all four sides of a trapezoid, calculating the area can be complex, as different configurations may yield various areas. However, with additional details, such as which sides are bases, you can apply relevant formulas to find the area.