All GMAT Math Resources
Example Questions
Example Question #1 : Calculating The Area Of A Quadrilateral
What is the area of a trapezoid with a height of 7, a base of 5, and another base of 13?
Example Question #2 : Calculating The Area Of A Quadrilateral
A circle can be circumscribed about each of the following figures except:
Each of the figures given in the other choices can have a circle circumscribed about it.
A triangle with sides 30, 40, 50.
A triangle
A regular pentagon
A regular hexagon
Each of the figures given in the other choices can have a circle circumscribed about it.
A circle can be circumscribed about any triangle regardless of its sidelengths or angle measures, so we can eliminate the two triangle choices.
A circle can be circumscribed about any regular polygon, so we can eliminate those two choices as well.
The correct choice is that each figure can have a circle circumscribed about it.
Example Question #2 : Calculating The Area Of A Quadrilateral
What is the area of a quadrilateral on the coordinate plane with vertices ?
As can be seen from this diagram, this is a parallelogram with base 8 and height 4:
The area of this parallelogram is the product of its base and its height:
Example Question #3 : Calculating The Area Of A Quadrilateral
What is the area of a quadrilateral on the coordinate plane with vertices ?
As can be seen in this diagram, this is a trapezoid with bases 10 and 5 and height 8.
Setting in the following formula, we can calculate the area of the trapezoid:
Example Question #5 : Calculating The Area Of A Quadrilateral
Note: Figure NOT drawn to scale
What is the area of Quadrilateral , above?
Quadrilateral is a composite of two right triangles, and , so we find the area of each and add the areas. First, we need to find and , since the area of a right triangle is half the product of the lengths of its legs.
By the Pythagorean Theorem:
Also by the Pythagorean Theorem:
The area of is .
The area of is .
Add the areas to get , the area of Quadrilateral .
Example Question #3 : Calculating The Area Of A Quadrilateral
What is the area of the quadrilateral on the coordinate plane with vertices ?
The quadrilateral formed is a trapezoid with two horizontal bases. One base connects (0,0) and (9,0) and therefore has length ; the other connects (4,7) and (7,7) and has length . The height is the vertical distance between the two bases, which is the difference of the coorindates: . Therefore, the area of the trapezoid is
Example Question #6 : Calculating The Area Of A Quadrilateral
What is the area of the quadrilateral on the coordinate plane with vertices .
The quadrilateral is a trapezoid with horizontal bases; one connects and and has length , and the other connects and and has length . The height is the vertical distance between the bases, which is the difference of the -coordinates; this is . Substitute in the formula for the area of a trapezoid:
Example Question #5 : Other Quadrilaterals
What is the area of the quadrilateral on the coordinate plane with vertices ?
The quadrilateral is a parallelogram with two vertical bases, each with length . Its height is the distance between the bases, which is the difference of the -coordinates: . The area of the parallelogram is the product of its base and its height:
Example Question #2 : Calculating The Area Of A Quadrilateral
Give the area of the above parallelogram if .
Multiply height by base to get the area.
By the 45-45-90 Theorem,
.
Since the product of the height and the base of a parallelogram is its area,
Example Question #3 : Calculating The Area Of A Quadrilateral
Give the area of the above parallelogram if .
Multiply height by base to get the area.
By the 30-60-90 Theorem:
.
The area is therefore