Finding the perimeter of a trapezoid: formula and tasks

In this publication, we will consider how to calculate the perimeter of a trapezoid and analyze examples of solving problems.

Perimeter Formula

The perimeter (P) of a trapezoid is equal to the sum of the lengths of all its sides.

P = a + b + c + d

• b и d – the base of the trapezoid;
• a и с – its sides.

Perimeter of an isosceles trapezoid

In an isosceles trapezoid, the sides are equal (a uXNUMXd c), which is why it is also called isosceles. The perimeter is calculated like this:

P =  2a + b + d or P = 2с + b + d

Perimeter of a rectangular trapezoid

To calculate the perimeter, the same formula is used as for a scalene trapezoid.

P = a + b + c + d

Examples of tasks

Task 1

Find the perimeter of a trapezoid if its bases are 7 cm and 10 cm and its sides are 4 cm and 5 cm.

Decision:

We use the standard formula, substituting the known side lengths into it: P u7d 10 cm + 4 cm + 5 cm + 26 cm uXNUMXd XNUMX cm.

Task 2

The perimeter of an isosceles trapezoid is 22 cm. Find the length of the side if the bases of the figure are 3 cm and 9 cm.

Decision:

As we know, the perimeter of an isosceles trapezoid is calculated by the formula: P = 2a + b + dWhere а – side.

Its length multiplied by two is: 2a = P – b – d = 22 cm – 3 cm – 9 cm = 10 cm.

Therefore, the length of the side is: a = 10 cm / 2 = 5 cm.