SSAT Upper Level Math : Area of Polygons
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Example Questions
Example Question #82 : Areas And Perimeters Of Polygons
The above diagram shows a rectangular solid. The shaded side is a square. Give the total surface area of the solid.
A square has four sides of equal length, as seen in the diagram below.
All six sides are rectangles, so their areas are equal to the products of their dimensions:
Top, bottom, front, back (four surfaces):
Left, right (two surfaces):
The total area:
Example Question #82 : Areas And Perimeters Of Polygons
The above diagram shows a rectangular solid. The shaded side is a square. In terms of 
Since a square has four sides of equal length, the solid looks like this:
The areas of each of the individual surfaces, each of which is a rectangle, are the product of their dimensions:
Front, back, top, bottom (four surfaces):
Left, right (two surfaces):
The total surface area is therefore
Example Question #53 : Area Of Polygons
Figure NOT drawn to scale
The above figure shows Rhombus 
Give the area of Rectangle 
A rhombus, by definition, has four sides of equal length. Therefore, 
Also, both 
The figure, with the lengths, is below.
The area of the entire Rhombus 
Rectangle 
From the Division Property, it follows that
and
This makes 450 the area of Rectangle
Example Question #2 : Area Of A Parallelogram
A parallelogram has the base length of 
The area of a parallelogram is given by:
Where 
Example Question #51 : Area Of Polygons
A parallelogram has a base length of 
Base length is 
The area of a parallelogram is given by:
Where:
So we can write:
Example Question #1 : Area Of A Parallelogram
The length of the shorter diagonal of a rhombus is 40% that of the longer diagonal. The area of the rhombus is 
Let 
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up, and solve for 
Example Question #4 : Area Of A Parallelogram
The length of the shorter diagonal of a rhombus is two-thirds that of the longer diagonal. The area of the rhombus is 
Let 
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up the following equation and solve for
To convert yards to inches, multiply by 36:
Example Question #52 : Area Of Polygons
The longer diagonal of a rhombus is 20% longer than the shorter diagonal; the rhombus has area 
Let 
of 
The area of a rhombus is half the product of the lengths of its diagonals, so we can set up an equation and solve for
Example Question #53 : Area Of Polygons
Which of the following shapes is NOT a quadrilateral?
Rhombus
Square
Triangle
Rectangle
Kite
Triangle
A quadrilateral is any two-dimensional shape with 
Example Question #2 : Shape Properties
What is the main difference between a square and a rectangle?
The sum of their angles
The number of sides they each have
Their side lengths
Their color
Their angle measurments
Their side lengths
The only difference between a rectangle and a square is their side lengths. A square has to have 
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