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

## Example Questions

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

A triangle has base 80 inches and area 4,200 square inches. What is its height?

Possible Answers:

Correct answer:

Explanation:

Use the area formula for a triangle, setting :

inches

### Example Question #15 : Triangles

The sum of the lengths of the legs of an isosceles right triangle is one meter. What is its area in square centimeters?

Possible Answers:

It is impossible to determine the area from the information given

Correct answer:

Explanation:

The legs of an isosceles right triangle have equal length, so, if the sum of their lengths is one meter, which is equal to 100 centimeters, each leg measures half of this, or

centimeters.

The area of a triangle is half the product of its height and base; for a right triangle, the legs serve as height and base, so the area of the triangle is

square centimeters.

### Example Question #2 : How To Find The Area Of A Triangle

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

has area . What is the area of Square  ?

Possible Answers:

Correct answer:

Explanation:

Since , and  are the midpoints of , and , if we call  the length of each side of the square, then

The area of  is half the product of the lengths of its legs:

The area of the square is the square of the length of a side, which is . This is eight times the area of , so the correct choice is

### Example Question #3 : How To Find The Area Of A Triangle

Which of the following is the greater quantity?

(a) The area of the above triangle

(b) 800

Possible Answers:

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

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

which is less than 800.

### Example Question #4 : How To Find The Area Of A Triangle

The above figure gives the lengths of the three sides of the triangle in feet. 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, which here are  feet and  feet.

Multiply each length by 12 to convert to inches - the lengths become  and . The area in square inches is therefore

square inches.

### Example Question #19 : Triangles

Figure NOT drawn to scale

Square  has area 1,600. . Which of the following is the greater quantity?

(a) The area of

(b) The area of

Possible Answers:

(a) and (b) are equal

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

Square  has area 1,600, so the length of each side is .

Since ,

Therefore, .

has as its area  has as its area .

Since  and , it follows that

and

has greater area than .

### Example Question #5 : How To Find The Area Of A Triangle

Figure NOT drawn to scale.

In the above diagram, Square  has area 400. Which is the greater quantity?

(a) The area of

(b) The area of

Possible Answers:

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

Square  has area 400, so its common sidelength is the square root of 400, or 20. Therefore,

.

The area of a right triangle is half the product of the lengths of its legs.

has legs  and , so its area is

.

has legs  and , so its area is

.

has the greater area.

### Example Question #5 : How To Find The Area Of A Triangle

Figure NOT drawn to scale

The above diagram depicts Parallelogram . Which is the greater quantity?

(a) The area of

(b) The area of

Possible Answers:

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

Opposite sides of a parallelogram have the same measure, so

Base  of  and base  of  have the same length;  also, as can be seen below, both have the same height, which is the height of the parallelogram.

Therefore, the areas of  and  have the same area - .

### Example Question #6 : How To Find The Area Of A Triangle

Refer to the above figure. Which is the greater quantity?

(a) The perimeter of the triangle

(b) 3 feet

Possible Answers:

(b) is the greater quantity

It is impossible to determine which quantity is the greater from the information given

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

(b) is the greater quantity

Explanation:

The perimeter of the triangle - the sum of the lengths of its sides - is

inches.

3 feet are equivalent to  inches, so this is the greater quantity.