SAT II Math II : Area

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

Example Question #11 : Area

Find the area of a triangle with a base length of  and a height of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a triangle.

Substitute the dimensions.

The answer is:  

Example Question #11 : Geometry

Find the area of a circle with a radius of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a circle.

Substitute the radius into the equation.

The area is:  

Example Question #314 : Sat Subject Test In Math Ii

Determine the area of a rectangle if the length is  and the height is .

Possible Answers:

Correct answer:

Explanation:

The area of a rectangle is:  

Substitute the length and height into the formula.

We will move the constant to the front and apply the FOIL method to simplify the binomials.

Distribute the fraction through all the terms of the trinomial.

The answer is:  

Example Question #315 : Sat Subject Test In Math Ii

What's the area of triangle with a side of  and a height of ?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a triangle.

Substitute the dimensions.

Use the FOIL method to expand this.

Simplify the terms.

Combine like-terms.

The answer is:  

Example Question #12 : Area

Determine the side of a square with an area of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a square.

Substitute the area into the equation.

Square root both sides.

The answer is:  

Example Question #13 : Area

Find the area of a circle with a radius of .

Possible Answers:

Correct answer:

Explanation:

The area of a circle is .

Substitute the radius and solve for the area.

The answer is:  

Example Question #12 : Geometry

Determine the area of a triangle with a base of 6, and a height of .

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a triangle.

Substitute the base and height into the equation.

The answer is:  

Example Question #13 : Geometry

Find the area of a circle with a diameter of .

Possible Answers:

Correct answer:

Explanation:

Divide the diameter by two.  This will be the radius.

Write the formula for the area of a circle.

The answer is:  

Example Question #323 : Sat Subject Test In Math Ii

Hexagon

In the provided diagram, hexagon  is regular;  and  are the midpoints of their respective sides. The perimeter of the hexagon is ; what is the area of Quadrilateral ?

Possible Answers:

Correct answer:

Explanation:

Quadrilateral  is a trapezoid, so we need to find the lengths of its bases and its height.

The perimeter of the hexagon is , so each side of the hexagon measures one sixth of this, or .

Construct the diameters of the hexagon, which meet at center ; construct the apothem from  to , with point of intersection . The diagram is below:

 Hexagon

 

The six triangles formed by the diameters are equilateral, so , and . Quadrilateral  is a trapezoid with bases of length 10 and 20. Since  has its endpoints at the midpoints of the legs of Trapezoid , it follows that  is a midsegment, and has as its length .

The trapezoid has bases of length  and ; we now need to find its height. This is the measure of , which is half the length of apothem  is the height of an equilateral triangle  and, consequently, the long leg of a right triangle . By the 30-60-90 Theorem, 

.

 

The area of a trapezoid of height  and base lengths  and  is

;

Setting :

  

Example Question #14 : Area

To the nearest whole, give the area of a regular pentagon with a perimeter of fifty.

Possible Answers:

Correct answer:

Explanation:

In a regular pentagon, called Pentagon , construct the five perpendicular segments from each vertex to its opposite side, as shown below:

Pentagon 2

The segments divide the pentagon into ten congruent triangles. 

In particular, examine , a radius of the pentagon, bisects , which, as the interior angle of a regular pentagon, has measure ; therefore,  is an apothem and therefore bisects ; since the pentagon has perimeter 50,  has length one fifth of this, or 10, and 

Using trigonometry,

or, substituting,

Solving for :

The area of this triangle is half the product of the lengths of legs  and :

Since the pentagon comprises ten triangles of this area, multiply:

To the nearest whole, this is 172.

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