### All HSPT Math Resources

## Example Questions

### Example Question #1 : Geometry

What is the area of a triangle with a base of 5 and a height of 20?

**Possible Answers:**

**Correct answer:**

When searching for the area of a triangle we are looking for the amount of the space enclosed by the triangle.

The equation for area of a triangle is

Plug in the numbers for base and height into the equation yielding

Then multiply the numbers together to arrive at the answer which is .

### Example Question #1 : Geometry

A trapezoid has height 32 inches and bases 25 inches and 55 inches. What is its area?

**Possible Answers:**

**Correct answer:**

Use the following formula, with :

### Example Question #1 : Geometry

What is the area of a triangle with a base of 22 cm and a height of 9 cm?

**Possible Answers:**

**Correct answer:**

Use the area of a triangle formula

Plug in the base and height. This gives you .

### Example Question #1 : How To Find The Area Of A Right Triangle

Right Triangle A has hypotenuse 25 inches and one leg of length 24 inches; Right Triangle B has hypotenuse 15 inches and one leg of length 9 inches; Rectangle C has length 16 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the width of Rectangle C?

**Possible Answers:**

**Correct answer:**

The area of a right triangle is half the product of its legs. In each case, we know the length of one leg and the hypotenuse, so we need to apply the Pythagorean Theorem to find the second leg, then take half the product of the legs:

Right Triangle A:

The length of the second leg is

inches.

The area is

square inches.

Right Triangle B:

The length of the second leg is

inches.

The area is

square inches.

The sum of the areas is square inches.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is inches.

### Example Question #40 : Right Triangles

Right Triangle A has legs of lengths 10 inches and 14 inches; Right Triangle B has legs of length 20 inches and 13 inches; Rectangle C has length 30 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the height of Rectangle C?

**Possible Answers:**

Insufficient information is given to determine the height.

**Correct answer:**

The area of a right triangle is half the product of its legs. The area of Right Triangle A is equal to square inches; that of Right Triangle B is equal to square inches. The sum of the areas is square inches, which is the area of Rectangle C.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is inches.

### Example Question #1 : 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 #2 : 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 A Parallelogram

Find the area of the following parallelogram:

Note: The formula for the area of a parallelogram is .

**Possible Answers:**

**Correct answer:**

The base of the parallelogram is 10, while the height is 5.

### Example Question #1 : How To Find The Area Of A Parallelogram

Find the area:

**Possible Answers:**

**Correct answer:**

The area of a parallelogram can be determined using the following equation:

Therefore,

### Example Question #1 : How To Find The Area Of A Rectangle

What is the area of a rectangle with length and width ?

**Possible Answers:**

**Correct answer:**

The formula for the area, , of a rectangle when we are given its length, , and width, , is .

To calculate this area, just multiply the two terms.

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