Intermediate Geometry : How to find the area of a parallelogram

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #244 : Quadrilaterals

In the figure, the height of the parallelogram is half the height of the equilateral triangle. Find the area of the shaded region.

12

Possible Answers:

Correct answer:

Explanation:

First, we will need to find the height of the equilateral triangle.

13

Recall that the height of an equilateral triangle will cut the equilateral triangle into two congruent  triangles that have side lengths in the the following ratio: 

Use the given side length of the equilateral triangle in order to find the length of the height.

Now, find the area of the equilateral triangle.

Now, use the height of the equilateral triangle to find the height of the parallelogram.

Next, find the area of the parallelogram.

Now, from the figure, we can see that we will need to subtract the area of the parallelogram from the area of the triangle in order to find the area of the shaded region.

Solve and round to two decimal places.

 

Example Question #245 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

1

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #246 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

2

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #247 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

3

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #248 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

4

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #249 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

5

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #250 : Quadrilaterals

In the figure, the area of the parallelogram is . Find the length of the base.

6

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since the values of lengths of shapes can only be positive, we know that the base of the parallelogram must be .

Example Question #81 : Parallelograms

In the figure, the area of the parallelogram is . Find the length of the base.

7

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since lengths of bases and heights can only be positive, .

Notice that the length of the base is given by the expression . Substitute in the value of  to find the length of the base.

Example Question #82 : Parallelograms

In the figure, the area of the parallelogram is . Find the length of the base.

8

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since lengths of bases and heights can only be positive, .

Notice that the length of the base is given by the expression . Substitute in the value of  to find the length of the base.

Example Question #83 : Parallelograms

In the figure, the area of the parallelogram is . Find the length of the base.

8

Possible Answers:

Correct answer:

Explanation:

13

Recall how to find the area of a parallelogram:

Now, substitute in the area, base, and height values that are given by the question.

Expand this equation.

Now factor this equation.

Solve for .

Since lengths of bases and heights can only be positive, .

Notice that the length of the base is given by the expression . Substitute in the value of  to find the length of the base.

Learning Tools by Varsity Tutors