High School Math : Plane Geometry
Study concepts, example questions & explanations for High School Math
All High School Math Resources
Example Questions
Example Question #11 : Parallelograms
In the parallellogram, what is the value of 
Opposite angles are equal, and adjacent angles must sum to 180.
Therefore, we can set up an equation to solve for z:
(z – 15) + 2z = 180
3z - 15 = 180
3z = 195
z = 65
Now solve for x:
2z = x = 130°
Example Question #2 : Parallelograms
What is the area of a parallelogram with a base of 
To solve this question you must know the formula for the area of a parallelogram.
In this equation, 
Example Question #4 : Parallelograms
What is the area of a parallelogram with a base of 
To solve this question you must know the formula for the area of a parallelogram.
The formula is
So we can plug in the side length for both base and height to yield
Perform the multiplication to arrive at the answer of 
Example Question #3 : Parallelograms
Find the area of the following parallelogram:
Cannot be determined from the given information.
The formula for the area of a parallelogram is:
where 
In order to the find the height of the parallelogram, use the formula for a 
The left side of the parallelogram forms the following
Plugging in our values, we get:
Example Question #182 : Geometry
Find the area of the following parallelogram:
Use the Pythagorean Theorem to determine the length of the diagonal:
The area of the parallelogram is twice the area of the right triangles:
Example Question #1 : How To Find The Area Of A Parallelogram
Find the area of the following parallelogram:
The formula for the area of a parallelogram is
Use the formula for a 
Plugging in our values, we get:
Example Question #381 : Geometry
Two rectangles are similar. The perimeter of the first rectangle is 36. The perimeter of the second is 12. If the base length of the second rectangle is 4, what is the height of the first rectangle?
10
6
2
8
4
6
Solve for the height of the second rectangle.
Perimeter = 2B + 2H
12 = 2(4) + 2H
12 = 8 + 2H
4 = 2H
H = 2
If they are similar, then the base and height are proportionally equal.
B1/H1 = B2/H2
4/2 = B2/H2
2 = B2/H2
B2 = 2H2
Use perimeter equation then solve for H:
Perimeter = 2B + 2H
36 = 2 B2 + 2 H2
36 = 2 (2H2) + 2 H2
36 = 4H2 + 2 H2
36 = 6H2
H2 = 6
Example Question #1 : Rectangles
A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the perimeter of the rectangle?
10(x + 1)
6x2 + 5
5x + 10
6x2 + 10x
5x + 5
10(x + 1)
Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.
P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)
Example Question #1 : Rectangles
What is the perimeter of the below rectangle in simplest radical form?
7√27
10√3
4√3 + 2√27
5√3
10√3
The perimeter of a figure is the sum of the lengths of all of its sides. The perimeter of this figure is √27 + 2√3 + √27 + 2√3. But, √27 = √9√3 = 3√3 . Now all of the sides have the same number underneath of the radical symbol (i.e. the same radicand) and so the coefficients of each radical can be added together. The result is that the perimeter is equal to 10√3.
Example Question #1 : How To Find The Perimeter Of A Rectangle
A rectangle has an area of 56 square feet, and a width of 4 feet. What is the perimeter, in feet, of the rectangle?
Divide the area of the rectangle by the width in order to find the length of 14 feet. The perimeter is the sum of the side lengths, which in this case is 14 feet + 4 feet +14 feet + 4 feet, or 36 feet.
Certified Tutor
All High School Math Resources
