SAT Math : How to find the height of a triangle

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Equilateral Triangles

A triangle has a base of 5 cm and an area of 15 cm. What is the height of the triangle?

Possible Answers:

1.5 cm

5 cm

None of the above

3 cm

6 cm

Correct answer:

6 cm

Explanation:

The area of a triangle is (1/2)*base*height. We know that the area = 15 cm, and the base is 5 cm, so:

15 = 1/2 * 5 * height

3 = 1/2 * height

6 = height

Example Question #1 : Equilateral Triangles

Trapequi1

In the figure above, AB = AD = AE = BD = BC = CD = DE = 1. What is the distance from A to C?

Possible Answers:

Correct answer:

Explanation:

Trapequi2

Trapequi3

Trapequi4

Example Question #2 : Equilateral Triangles

A triangles has sides of 5, 9, and x. Which of the folowing CANNOT be a possible value of x?

Possible Answers:

5

7

6

3

4

Correct answer:

3

Explanation:

The sum of the lengths of the shortest sides of a triangle cannot be less than the third side.

3 + 5 = 8 < 9, so 3 can't be a value of x.

Example Question #2 : How To Find The Height Of A Triangle

An equilateral triangle has a side length of 4. What is the height of the triangle? 

Possible Answers:

Correct answer:

Explanation:

Because the triangle is an equilateral triangle, you know that all sides have the same length, so all sides have the length of 4. Draw the triangle and label all sides as 4. Next, draw a point in the middle of one of the sides, and label each side as 2. Draw a line segment from the midpoint that you just created to the opposite angle of the triangle. That line segment is the height of the triangle. You can solve for it by using the Pythagorean theorem.

The Pythagorean theorem states that

In our scenario a = 2, c = 4, and you are solving for b. After plugging the numbers into the formula you get

 

and then 

and then 

and then 

Therefore, the height of the triangle is  

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