### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #6 : Geometry

Give the area of the above triangle.

**Possible Answers:**

**Correct answer:**

By Heron's formula, the area of a triangle given its sidelengths is

Where are the sidelengths and

,

or half the perimeter.

Setting ,

Therefore,

### Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle

Give the area of the above triangle.

**Possible Answers:**

**Correct answer:**

By Heron's formula, the area of a triangle given its sidelengths is

,

where are the sidelengths and

,

or half the perimeter.

Setting ,

.

Therefore,

### Example Question #1 : How To Find The Area Of An Acute / Obtuse Triangle

The base of the triangle is . The height of the triangle is a multiple of between and . What is the area of the triangle?

**Possible Answers:**

**Correct answer:**

First, find the height of the triangle by listing out the multiples of .

Since is the only multiple of that is between and , it must be the height.

Now, find the area of the triangle.

### Example Question #2 : How To Find The Area Of An Acute / Obtuse Triangle

The base of an obtuse triangle is , and the height is . What is the area of the triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #3 : How To Find The Area Of An Acute / Obtuse Triangle

The height of an acute triangle is , and the base is . What is the area of this triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #4 : How To Find The Area Of An Acute / Obtuse Triangle

The base of a triangle is , and the height is . In terms of , what is the area of the triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #5 : How To Find The Area Of An Acute / Obtuse Triangle

The base of a triangle is , and the height is . What is the area of this triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #6 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base is . In terms of , what is the area of the triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #7 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base of the triangle is . In terms of , what is the area of the triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .

### Example Question #8 : How To Find The Area Of An Acute / Obtuse Triangle

The height of a triangle is , and the base is . What is the area of the triangle?

**Possible Answers:**

**Correct answer:**

Use the following formula to find the area of a triangle:

Now, substitute in for the base and for the height.

The area of the triangle is .