How to find the perimeter of a trapezoid

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Math › How to find the perimeter of a trapezoid

Questions 1 - 6

1

Determine the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.39.24_pm

Explanation

The formula for the perimeter of a trapezoid is:

,

where is the length of the base and is the length of the edge.

Plugging in our values, we get:

2

Find the perimeter of the following trapezoid:

Trapezoid

Explanation

The formula for the perimeter of a trapezoid is:

$P= b_{1} +b_{2}+e_{1}+e_{2}$

Where is the base and is the edge

Plugging in our values, we get:

3

Find the perimeter of the following trapezoid:

$35+5\sqrt{2}+5\sqrt{3}\ m$

$15+5\sqrt{2}+5\sqrt{3}\ m$

$35+10\sqrt{2}+5\sqrt{3}\ m$

$35+5\sqrt{2}+10\sqrt{3}\ m$

$15+5\sqrt{2}+10\sqrt{3}\ m$

Explanation

The formula for the perimeter of a trapezoid is

.

Use the formula for a triangle to find the length of the base and side:

$a-2a-a\sqrt{3}$

$5\ m-10\ m-5\sqrt{3}\ m$

Use the formula for a triangle to find the length of the base and side:

$5\ m-5\ m-5\sqrt{2}\ m$

Plugging in our values, we get:

$P = 5\sqrt{2}\ m+10\ m+10\ m+5\sqrt{3}\ m+10\ m+5\ m$

$P = 35+5\sqrt{2}+5\sqrt{3}\ m$

4

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.)?

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.

5

Find the perimeter of the following trapezoid:

Screen_shot_2014-02-27_at_6.47.22_pm

Explanation

The formula for the perimeter of a trapezoid is:

,

where is the length of the base and is the length of the edge.

Plugging in our values, we get:

6

Find the perimeter of the following trapezoid:

Trapezoid_angles

$44+12\sqrt{3}m$

$56+12\sqrt{3}m$

$44+6\sqrt{3}m$

Explanation

Use the formula for triangles in order to find the lengths of all the sides and bases.

The formula is:

$a-a\sqrt{3}-2a$

Where is the length of the side opposite the $\measuredangle 30$ .

Beginning with the side, if we were to create a triangle, the length of the base is $6\sqrt{3}m$ , and the height is .

Creating another triangle on the left, we find the height is , the length of the base is $2\sqrt{3}m$ , and the side is $4\sqrt{3}m$ .

The formula for the perimeter of a trapezoid is:

$P= b_{1} +b_{2}+e_{1}+e_{2}$

Where is the base and is the edge

Plugging in our values, we get:

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

$P=44+12\sqrt{3}m$

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