High School Math : How to find the perimeter of a trapezoid

Study concepts, example questions & explanations for High School Math

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : How To Find The Perimeter Of A Trapezoid

This figure is an isosceles trapezoid with bases of 6 in and 18 in and a side of 10 in.Isoceles_trapezoid

What is the perimeter of the isoceles trapezoid (in.)?

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 44\)

\(\displaystyle 56\)

\(\displaystyle 96\)

\(\displaystyle 34\)

Correct answer:

\(\displaystyle 44\)

Explanation:

The perimeter of the isoceles trapezoid is the sum of all the sides.  You can assume the left side is also 10 in. because it is an isoceles trapezoid. 

\(\displaystyle 6+18+10+10=44\)

Example Question #171 : Plane Geometry

Find the perimeter of the following trapezoid:

Trapezoid

Possible Answers:

\(\displaystyle 68m\)

\(\displaystyle 72m\)

\(\displaystyle 70m\)

\(\displaystyle 62m\)

\(\displaystyle 64m\)

Correct answer:

\(\displaystyle 68m\)

Explanation:

The formula for the perimeter of a trapezoid is:

\(\displaystyle P= b_{1} +b_{2}+e_{1}+e_{2}\)

Where \(\displaystyle b\) is the base and \(\displaystyle e\) is the edge

Plugging in our values, we get:

\(\displaystyle P= 16m +26m+13m+13m=68m\)

Example Question #2 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the following trapezoid:

Trapezoid_angles

Possible Answers:

\(\displaystyle 44+6\sqrt{3}m\)

\(\displaystyle 56+12\sqrt{3}m\)

\(\displaystyle 44+12\sqrt{3}m\)

\(\displaystyle 56m\)

\(\displaystyle 44m\)

Correct answer:

\(\displaystyle 44+12\sqrt{3}m\)

Explanation:

Use the formula for \(\displaystyle 30-60-90\) triangles in order to find the lengths of all the sides and bases.

The formula is:

\(\displaystyle a-a\sqrt{3}-2a\)

Where \(\displaystyle a\) is the length of the side opposite the \(\displaystyle \measuredangle 30\).

Beginning with the \(\displaystyle 12m\) side, if we were to create a \(\displaystyle 30-60-90\) triangle, the length of the base is \(\displaystyle 6\sqrt{3}m\), and the height is \(\displaystyle 6m\).

Creating another \(\displaystyle 30-60-90\) triangle on the left, we find the height is \(\displaystyle 6m\), the length of the base is \(\displaystyle 2\sqrt{3}m\), and the side is \(\displaystyle 4\sqrt{3}m\).

 

The formula for the perimeter of a trapezoid is:

\(\displaystyle P= b_{1} +b_{2}+e_{1}+e_{2}\)

Where \(\displaystyle b\) is the base and \(\displaystyle e\) is the edge

Plugging in our values, we get:

\(\displaystyle P= (16m) +(16m+6\sqrt{3}m+2\sqrt{3}m)+(12m)+(4\sqrt{3}m)\)

\(\displaystyle P=44+12\sqrt{3}m\)

Example Question #3 : How To Find The Perimeter Of A Trapezoid

Determine the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.39.24_pm

Possible Answers:

\(\displaystyle 28m\)

\(\displaystyle 20m\)

\(\displaystyle 21m\)

\(\displaystyle 25m\)

\(\displaystyle 24m\)

Correct answer:

\(\displaystyle 21m\)

Explanation:

The formula for the perimeter of a trapezoid is:

\(\displaystyle P=b_1+b_2+e_1+e_2\),

where \(\displaystyle b\) is the length of the base and \(\displaystyle e\) is the length of the edge.

Plugging in our values, we get:

\(\displaystyle P=7m+5m+4m+5m=21m\)

Example Question #4 : How To Find The Perimeter Of A Trapezoid

Find the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.47.22_pm

Possible Answers:

\(\displaystyle 90m\)

\(\displaystyle 70m\)

\(\displaystyle 80m\)

\(\displaystyle 88m\)

\(\displaystyle 78m\)

Correct answer:

\(\displaystyle 88m\)

Explanation:

The formula for the perimeter of a trapezoid is:

\(\displaystyle P=b_1+b_2+e_1+e_2\),

where \(\displaystyle b\) is the length of the base and \(\displaystyle e\) is the length of the edge.

Plugging in our values, we get:

\(\displaystyle P=20m+18m+20m+30m=88m\)

Example Question #21 : Quadrilaterals

Find the perimeter of the following trapezoid:

19

Possible Answers:

\(\displaystyle 35+5\sqrt{2}+5\sqrt{3}\ m\)

\(\displaystyle 15+5\sqrt{2}+10\sqrt{3}\ m\)

\(\displaystyle 35+10\sqrt{2}+5\sqrt{3}\ m\)

\(\displaystyle 15+5\sqrt{2}+5\sqrt{3}\ m\)

\(\displaystyle 35+5\sqrt{2}+10\sqrt{3}\ m\)

Correct answer:

\(\displaystyle 35+5\sqrt{2}+5\sqrt{3}\ m\)

Explanation:

The formula for the perimeter of a trapezoid is

\(\displaystyle P = base_1+base_2+side_1+side_2\).

Use the formula for a \(\displaystyle 30-60-90\) triangle to find the length of the base and side:

\(\displaystyle a-2a-a\sqrt{3}\)

\(\displaystyle 5\ m-10\ m-5\sqrt{3}\ m\) 

Use the formula for a \(\displaystyle 45-45-90\) triangle to find the length of the base and side:

\(\displaystyle a-a-2a\)

\(\displaystyle 5\ m-5\ m-5\sqrt{2}\ m\) 

Plugging in our values, we get:

\(\displaystyle P = 5\sqrt{2}\ m+10\ m+10\ m+5\sqrt{3}\ m+10\ m+5\ m\)

\(\displaystyle P = 35+5\sqrt{2}+5\sqrt{3}\ m\)

Learning Tools by Varsity Tutors