ISEE Middle Level Math : How to find the area of a triangle

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #263 : Geometry

The three angles of a triangle are labeled , , and . If  is , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Given that the three angles of a triangle always add up to 180 degrees, the following equation can be used:

Example Question #43 : Triangles

In an equilateral triangle, which of the following is NOT true?

Possible Answers:

All angles are equal

All sides are equal

There is a 60 degree angle

There is a 90 degree angle

Correct answer:

There is a 90 degree angle

Explanation:

In an equilateral triangle, all sides and angles are equal. All the angles equal 60 degrees, so there is a 60 degree angle.

Therefore, the answer choice, “There is a 90 degree angle” is not true and is the correct answer choice. 

Example Question #1821 : Hspt Mathematics

The hypotenuse of a right triangle is  feet; it has one leg  feet long. Give its area in square inches.

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set :

The legs have length  and  feet; multiply both dimensions by  to convert to inches:

 inches

 inches.

Now find half the product:

Example Question #44 : Triangles

What is the area (in square feet) of a triangle with a base of  feet and a height of  feet?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by

 

Example Question #45 : Triangles

What is the area of a triangle with a base of  and a height of ?

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is \dpi{100} Area=\frac{1}{2}\times base\times height.

Plug the given values into the formula to solve:

\dpi{100} Area=\frac{1}{2}\times 12\times 3

\dpi{100} Area=\frac{1}{2}\times 36

\dpi{100} Area=18

Example Question #46 : Triangles

You have two traingular gardens next to each other.  They both have a base of  and a height of .  What is the total area?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is 

 

and since there are two identical traingles, them put together will just be 

.  

So your answer will just be .

Example Question #47 : Triangles

Pentagon

The above figure depicts Square  with perimeter 240. , and  are the midpoints of , and , respectively.

Give the area of Polygon .

Possible Answers:

Correct answer:

Explanation:

Square  has perimeter 240, so the length of each side is one fourth of this, or 

.

Segment , as seen below, divides Polygon  into two figures:

Pentagon 1

One figure is , with base and height 60 and 30, respectively. Its area is half their product, or 

The other figure is Rect , whose length and width are 60 and 30, respectively. Its area is their product, or

Add these areas:

.

Example Question #11 : How To Find The Area Of A Triangle

Right triangle 3

Give the area of the above triangle.

Possible Answers:

Correct answer:

Explanation:

The area of a right triangle is half the product of the lengths of its legs, which here are 25 and 60. So

Example Question #12 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 10cm and a height that is half the base.

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, we will use the following formula:

 

Now, we know the base has a length of 10cm.  We also know the height is half the base.  Therefore, the height is 5cm.  Knowing this, we can substitute into the formula.  We get

Example Question #13 : How To Find The Area Of A Triangle

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

Possible Answers:

Correct answer:

Explanation:

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

To find the area of a triangle, use the following:

Where b and h are the base and height.

In this case, we are told that the base and height are both 50 meters, thus, the perimeter will be:

So our answer is:

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