GMAT Math : Calculating the area of an acute / obtuse triangle

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #1 : Calculating The Area Of An Acute / Obtuse Triangle

What is the area, to the nearest whole square inch, of a triangle with sides 12, 13, and 15 inches?

Possible Answers:

None of the other answers are correct.

Correct answer:

Explanation:

Use Heron's formula:

where , and

Example Question #2 : Calculating The Area Of An Acute / Obtuse Triangle

Calculate the area of the triangle (not drawn to scale).

Possible Answers:

Correct answer:

Explanation:

In this problem, the base is 12 and the height is 6. Therefore:

Example Question #3 : Calculating The Area Of An Acute / Obtuse Triangle

Arrow

Note: Figure NOT drawn to scale.

What is the area of the above figure?

Possible Answers:

More information is needed to answer this question.

Correct answer:

Explanation:

The figure is a composite of a rectangle and a triangle, as shown:

Split_arrow

The rectangle has area 

The triangle has area 

The total area of the figure is 

Example Question #2 : Calculating The Area Of An Acute / Obtuse Triangle

Which of the following cannot be the measure of the vertex angle of an isosceles triangle?

Possible Answers:

Each of the other choices can be the measure of the vertex angle of an isosceles triangle.

Correct answer:

Each of the other choices can be the measure of the vertex angle of an isosceles triangle.

Explanation:

The only restriction on the measure of the vertex angle of an isosceles triangle is the restriction on any angle of a triangle - that it fall between  and , noninclusive. If  is any number in that range, each base angle, the two being congruent, will measure , which will fall in the acceptable range.

Since all of these measures fall in that range, the correct response is that all are allowed.

Example Question #5 : Calculating The Area Of An Acute / Obtuse Triangle

What is the area of the triangle on the coordinate plane formed by the -axis and the lines of the equations  and  ?

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve this is to graph the three lines and to observe the dimensions of the resulting triangle. It helps to know the coordinates of the three points of intersection, which we can do as follows:

The intersection of  and the -axis - that is, the line  can be found with some substitution:

The lines intersect at 

 

The intersection of  and the  -axis can be found the same way:

 

These lines intersect at 

 

The intersection of  and   can be found via the substitution method:

The lines intersect at 

 

The triangle therefore has these three vertices. It is shown below.

Triangle

As can be seen, it is a triangle with base 9 and height 12, so its area is 

Example Question #5 : Calculating The Area Of An Acute / Obtuse Triangle

What is the area of a triangle on the coordinate plane with its vertices on the points  ?

Possible Answers:

Correct answer:

Explanation:

The vertical segment connecting  and  can be seen as the base of this triangle; this base has length . The height is the perpendicular (horizontal) distance from  to this segment, which is 6, the same as the -coordinate of this point. The area of the triangle is therefore 

.

Example Question #3 : Calculating The Area Of An Acute / Obtuse Triangle

Which of the following is the area of a triangle on the coordinate plane with its vertices on the points  , where  ?

Possible Answers:

Correct answer:

Explanation:

We can view the horizontal segment connecting , and  as the base; its length wiill be . The height will be the perpendicular (vertical) distance to this segment from the opposite point , which is , the -coordinate; therefore, the area of the triangle will be half the product of these two numbers, or

.

Example Question #4 : Calculating The Area Of An Acute / Obtuse Triangle

Give the area of a triangle on the coordinate plane with vertices .

Possible Answers:

Correct answer:

Explanation:

This can be illustrated by showing this triangle inscribed inside a rectangle whose vertices are :

Triangle

The area of the white triangle  is the one whose area we calculate. To do this, we need the area of the square:

The area of the red triangle:

The area of the green triangle:

And the area of the beige triangle:

The area of the white triangle will be as follows:

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