All Advanced Geometry Resources
Example Questions
Example Question #21 :Trapezoids
Find the area of the figure below.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #22 :How To Find The Area Of A Trapezoid
Find the area of the figure.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #23 :How To Find The Area Of A Trapezoid
Find the area of the figure.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #31 :Trapezoids
Find the area of the figure below.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #32 :Trapezoids
Find the area of the figure below.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #33 :Trapezoids
Find the area of the figure below.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #34 :Trapezoids
Find the area of the figure below.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #35 :Trapezoids
Find the area of the figure.
From the figure, you should notice that it is made up of a right triangle and a trapezoid. The lower base of the trapezoid is also the hypotenuse of the right triangle.
First, find the length of the hypotenuse of the right triangle using the Pythagorean Theorem.
Next, use this value to find the area of the trapezoid.
Plug in the given and found values to find the area.
Next, find the area of the triangle.
To find the area of the figure, add the two areas together.
Make sure to round toplaces after the decimal.
Example Question #36 :Trapezoids
Figure NOT drawn to scale.
Examine the above trapezoid.
,,
True, false, or inconclusive: the area of Trapezoidis 200.
False
True
True
The area of a trapezoid is equal to one half the product of half the height of the trapezoid and the sum of the lengths of the bases. This is
or, equivalently,
The height of the trapezoid is
.
The lengths of basesandare not given, so it might appear that determining the area of the trapezoid is impossible.
However, it is given thatand- that is, the segmentbisects both legs of the trapezoid. This makesthe midsegment of the trapezoid, the length of which is the arithmetic mean of those of the bases:
.
Therefore, the formula for the area of the trapezoid can be rewritten as
,
the product of the height and the length of the midsegment.
and, so
,
making the statement true.
Example Question #1 :How To Find The Length Of The Diagonal Of A Trapezoid
What is the length of the diagonals of trapezoid? Assume the figure is an isoceles trapezoid.
To find the length of the diagonal, we need to use the Pythagorean Theorem. Therefore, we need to sketch the following triangle within trapezoid:
We know that the base of the triangle has length. By subtracting the top of the trapezoid from the bottom of the trapezoid, we get:
Dividing by two, we have the length of each additional side on the bottom of the trapezoid:
Adding these two values together, we get.
The formula for the length of diagonaluses the Pythagoreon Theorem:
, whereis the point betweenandrepresenting the base of the triangle.
Plugging in our values, we get: