### All ISEE Middle Level Math Resources

## 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:**

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

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:**

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:**

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:**

The formula for the area of a triangle is .

Plug the given values into the formula to solve:

### 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:**

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

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

Give the area of Polygon .

**Possible Answers:**

**Correct answer:**

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:

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

Give the area of the above triangle.

**Possible Answers:**

**Correct answer:**

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:**

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:**

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: