Perimeter of a Trapezoid with a Missing Side
The perimeter of a trapezoid can be calculated even if there are not enough sides. In such cases, you can use the given sides of the trapezoid, apply the Pythagoras theorem and other properties to find the missing sides, and then calculate the perimeter.
Example: Find the perimeter of the trapezoid PQRS with dimensions PQ = 110 m, SV = 40 m, VU = 110 m, UR = 70 m, QU = 80 m.
Solution:
Use the given dimensions to find the missing length of PS and QR
Step 1: If we take the △QUR, we get QU = 80m and UR = 70m. We can see that △QUR is a right-angled triangle. So we can use the Pythagoras theorem to calculate the QR value.
Step 2: According to the Pythagoras theorem, QR2 = QU2 + UR2. This means
QR2 = 802 + 702
QR2 = 6400 + 4900
QR = √11300 = 106.301 m
Step 3: Since QU = 80m, PQ is parallel to SR, so PV is also 80m, so we can now calculate the missing side PS of the trapezoid.
Step 4: Taking the right triangle △PSV, PV = 80m, SV = 40m, so applying the Pythagoras theorem we get PS2 = PV2 + SV2. This means
PS2 = 802 + 402
PS2 = 6400 + 1600
PS = √8000 = 89.44 m
Step 5: Now that we know all the faces of the trapezoid, we can add up all four faces to find the perimeter. This means that the perimeter of the trapezoid is PQRS
= PQ + QR + RS + SP
= 110 + 106.301 + 220 + 89.44
= 525.741 m
Thus, the missing side of the trapezoid is found.
Read More,
How to find the Perimeter of a Trapezoid?
Perimeter of the Trapezoid in Geometry is the sum of all the sides of the trapezoid. It is the length of all its boundaries and is measured in units of length, i.e. perimeter of the trapezoid is measured in cm, m, etc. A trapezoid is a quadrilateral that has a pair of parallel sides (lines). It is a quadrilateral whose perimeter is the sum of all the sides of a quadrilateral.
Here, in this article, we will learn about, What is a Trapezoid, the Perimeter of the trapezoid, the perimeter of the trapezoid formula, examples, and others in detail.
Table of Content
- What is a Trapezoid?
- What is the Perimeter Of Trapezoid?
- Perimeter of Trapezoid Formula
- How to Find Perimeter of a Trapezoid?
- Perimeter of a Trapezoid with a Missing Side
Contact Us