ISEE Lower Level Math : Triangles

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

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Example Questions

Example Question #31 : Triangles

Find the area of a triangle with a base of 9in and a height of 12in.

Possible Answers:

\displaystyle 108\text{in}^2

\displaystyle 33\text{in}^2

\displaystyle 27\text{in}^2

\displaystyle 54\text{in}^2

\displaystyle 21\text{in}^2

Correct answer:

\displaystyle 54\text{in}^2

Explanation:

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

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h

where b is the base and h is the height of the triangle.

 

Now, we know the base of the triangle is 9in.  We also know the height of the triangle is 12in.  

Knowing this, we can substitute into the formula  We get

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 9\text{in} \cdot 12\text{in}

Now, we can simplify things before we multiply to make things easier.  The 2 in the denominator of the fraction and the 12 can both be divided by 2. So, we get

\displaystyle \text{area of triangle} = \frac{1}{1} \cdot 9\text{in} \cdot 6\text{in}

\displaystyle \text{area of triangle} = 9\text{in} \cdot 6\text{in}

\displaystyle \text{area of triangle} = 54\text{in}^2

Example Question #1261 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Find the area of a triangle with a base of 4ft and a height that is two times the base.

Possible Answers:

\displaystyle 4\text{ft}^2

\displaystyle 16\text{ft}^2

\displaystyle 32\text{ft}^2

\displaystyle 8\text{ft}^2

\displaystyle 24\text{ft}^2

Correct answer:

\displaystyle 16\text{ft}^2

Explanation:

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

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h

where b is the base and h is the height of the triangle.

 

Now, we know the base of the triangle is is 4ft.  We also know the height of the triangle is two times the base.  Therefore, the height is 8ft. 

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 8\text{ft}

\displaystyle \text{area of triangle} = 2\text{ft} \cdot 8\text{ft}

\displaystyle \text{area of triangle} = 16\text{ft}^2

Example Question #1261 : Isee Lower Level (Grades 5 6) Mathematics Achievement

Use the following triangle to answer the question.

Triangle7

If the triangle has a height of 7cm, find the area.

Possible Answers:

\displaystyle 28\text{cm}^2

\displaystyle 24\text{cm}^2

\displaystyle 32\text{cm}^2

\displaystyle 14\text{cm}^2

\displaystyle 16\text{cm}^2

Correct answer:

\displaystyle 14\text{cm}^2

Explanation:

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

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h

where b is the base and h is the height of the triangle.

 

Now, given the triangle

Triangle7

We can see the base is 4cm.  We also know the height is 7cm.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 4\text{cm} \cdot 7\text{cm}

\displaystyle \text{area of triangle} = 2\text{cm} \cdot 7\text{cm}

\displaystyle \text{area of triangle} = 14\text{cm}^2

Example Question #31 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 9cm and a height of 8cm.

Possible Answers:

\displaystyle 17\text{cm}^2

\displaystyle 36\text{cm}^2

\displaystyle 36\text{cm}

\displaystyle 72\text{cm}^2

\displaystyle 72\text{cm}

Correct answer:

\displaystyle 36\text{cm}^2

Explanation:

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

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h

where b is the base and h is the height of the triangle.

 

Now, we know the base is 9cm and the height is 8cm.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 9\text{cm} \cdot 8\text{cm}

\displaystyle \text{area of triangle} = 9\text{cm} \cdot 4\text{cm}

\displaystyle \text{area of triangle} = 36\text{cm}^2

Example Question #35 : How To Find The Area Of A Triangle

The base of a triangle is \displaystyle 7 inches, and the height of the triangle is \displaystyle 3.5 inches. What is the area of the triangle?

Possible Answers:

\displaystyle 24.25 \displaystyle \textup{in.}^2

\displaystyle 24.5 \displaystyle \textup{in.}^2

\displaystyle 10.25 \displaystyle \textup{in.}^2

\displaystyle 12.20 \displaystyle \textup{in.}^2

\displaystyle 12.25 \displaystyle \textup{in.}^2

Correct answer:

\displaystyle 12.25 \displaystyle \textup{in.}^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

\displaystyle 7 * 3.5 = 24.5 

\displaystyle 24.5/2 = 12.25 

Example Question #36 : How To Find The Area Of A Triangle

The base of a triangle is \displaystyle 4.4 inches, and the height of the triangle is \displaystyle 2.3 inches. What is the area of the triangle?

Possible Answers:

\displaystyle 10.12 \displaystyle \textup{in.}^2

\displaystyle 5.12 \displaystyle \textup{in.}^2

\displaystyle 10.06 \displaystyle \textup{in.}^2

\displaystyle 5.06 \displaystyle \textup{in.}^2

\displaystyle 6.06 \displaystyle \textup{in.}^2

Correct answer:

\displaystyle 5.06 \displaystyle \textup{in.}^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

\displaystyle 4.4 * 2.3 = 10.12 

\displaystyle 10.12/2 = 5.06

Example Question #1263 : Isee Lower Level (Grades 5 6) Mathematics Achievement

The base of a triangle is \displaystyle 2.2 inches, and the height of the triangle is \displaystyle 1.1 inches. What is the area of the triangle?

 

Possible Answers:

\displaystyle 3.42\displaystyle \textup{in.}^2

\displaystyle 2.42\displaystyle \textup{in.}^2

\displaystyle 1.21\displaystyle \textup{in.}^2

\displaystyle 2.40\displaystyle \textup{in.}^2

\displaystyle 1.42\displaystyle \textup{in.}^2

Correct answer:

\displaystyle 1.21\displaystyle \textup{in.}^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

\displaystyle 2.2 * 1.1 = 2.42

\displaystyle 2.42/2 = 1.21

Example Question #1264 : Isee Lower Level (Grades 5 6) Mathematics Achievement

The base of a triangle is \displaystyle 5 inches, and the height of the triangle is \displaystyle 8 inches. What is the area of the triangle?

Possible Answers:

\displaystyle 15\displaystyle \textup{in.}^2

\displaystyle 40\displaystyle \textup{in.}^2

\displaystyle 30\displaystyle \textup{in.}^2

\displaystyle 20\displaystyle \textup{in.}^2

\displaystyle 25\displaystyle \textup{in.}^2

Correct answer:

\displaystyle 20\displaystyle \textup{in.}^2

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

\displaystyle 5 * 8 = 40

\displaystyle 40/2 = 20

Example Question #32 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

  • height:  9cm
  • base:   12cm
Possible Answers:

\displaystyle 36\text{cm}^2

\displaystyle 108\text{cm}^2

\displaystyle 72\text{cm}^2

\displaystyle 84\text{cm}^2

\displaystyle 54\text{cm}^2

Correct answer:

\displaystyle 54\text{cm}^2

Explanation:

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

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot b \cdot h

where b  is the base and h is the height of the triangle.

 

Now, we know the base of the triangle is 12in.  We also know the height of the triangle is 9in.

Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 12\text{in} \cdot 9\text{in}

\displaystyle \text{area of triangle} = 6\text{in} \cdot 9\text{in}

\displaystyle \text{area of triangle} = 54\text{in}^2

Example Question #332 : Geometry

Find the area of a triangle with a base of 6cm and a height that is two times the base.

Possible Answers:

\displaystyle 30\text{cm}^2

\displaystyle 48\text{cm}^2

\displaystyle 52\text{cm}^2

\displaystyle 72\text{cm}^2

\displaystyle 36\text{cm}^2

Correct answer:

\displaystyle 36\text{cm}^2

Explanation:

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

\displaystyle A = \frac{1}{2} \cdot b \cdot h

where b  is the base and h is the height of the triangle.

 

Now, we know the base of the triangle is 6cm.  We also know the height of the triangle is two times the base.  Therefore, the height is 12cm.

Knowing this, we can substitute into the formula.  We get

\displaystyle A = \frac{1}{2} \cdot 6\text{cm} \cdot 12\text{cm}

\displaystyle A = 3\text{cm} \cdot 12\text{cm}

\displaystyle A = 36\text{cm}^2

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