ISEE Middle Level Math : Triangles

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

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Example Questions

Example Question #22 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 17in and a height of 12in.

Possible Answers:

\(\displaystyle 121\text{in}^2\)

\(\displaystyle 144\text{in}^2\)

\(\displaystyle 41\text{in}^2\)

\(\displaystyle 102\text{in}^2\)

\(\displaystyle 29\text{in}^2\)

Correct answer:

\(\displaystyle 102\text{in}^2\)

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 17in.  We also know the height of the triangle is 12in.

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

\(\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 17\text{in} \cdot 12\text{in}\)

\(\displaystyle \text{area of triangle} = 17\text{in} \cdot 6\text{in}\)

\(\displaystyle \text{area of triangle} = 102\text{in}^2\)

Example Question #23 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

 

  •          Height:  13in
  •          Base:     8in
Possible Answers:

\(\displaystyle 96\text{in}^2\)

\(\displaystyle 36\text{in}^2\)

\(\displaystyle 48\text{in}^2\)

\(\displaystyle 104\text{in}^2\)

\(\displaystyle 52\text{in}^2\)

Correct answer:

\(\displaystyle 52\text{in}^2\)

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 is 8in.  We also know the height is 13in.  We can substitute into the formula. We get

\(\displaystyle A = \frac{1}{2} \cdot 8\text{in} \cdot 13\text{in}\)

\(\displaystyle A = 4\text{in} \cdot 13\text{in}\)

\(\displaystyle A = 52\text{in}^2\)

Example Question #24 : How To Find The Area Of A Triangle

Find the area of a triangle with the following measurements:

  • base = 8in
  • height = 7in
Possible Answers:

\(\displaystyle 15\text{in}^2\)

\(\displaystyle 36\text{in}^2\)

\(\displaystyle 56\text{in}^2\)

\(\displaystyle 24\text{in}^2\)

\(\displaystyle 28\text{in}^2\)

Correct answer:

\(\displaystyle 28\text{in}^2\)

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 is 8in and the height is 7in. Knowing this, we can substitute into the formula.  So, we get

\(\displaystyle A = \frac{1}{2} \cdot 8\text{in} \cdot 7\text{in}\)

\(\displaystyle A = 4\text{in} \cdot 7\text{in}\)

\(\displaystyle A = 28\text{in}^2\)

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

Find the area of a triangle with a base of 5cm and a height that is two times the base.

Possible Answers:

\(\displaystyle 15\text{cm}^2\)

\(\displaystyle 25\text{cm}^2\)

\(\displaystyle 20\text{cm}^2\)

\(\displaystyle 35\text{cm}^2\)

\(\displaystyle 50\text{cm}^2\)

Correct answer:

\(\displaystyle 25\text{cm}^2\)

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 is 5cm.  We know the height is two times the base.  Therefore, the height is 10cm.

So, we can substitute. 

 

\(\displaystyle A = \frac{1}{2} \cdot 5\text{cm} \cdot 10\text{cm}\)

\(\displaystyle A = 5\text{cm} \cdot 5\text{cm}\)

\(\displaystyle A = 25\text{cm}^2\)

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

Find the area of a triangle with a base of 12in and a height of 14in.

Possible Answers:

\(\displaystyle 168\text{in}^2\)

\(\displaystyle 84\text{in}^2\)

\(\displaystyle 122\text{in}^2\)

\(\displaystyle 40\text{in}^2\)

\(\displaystyle 38\text{in}^2\)

Correct answer:

\(\displaystyle 84\text{in}^2\)

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 12in.  We know the height of the triangle is 14in.  So, we can substitute.  We get

\(\displaystyle A = \frac{1}{2} \cdot 12\text{in} \cdot 14\text{in}\)

\(\displaystyle A = 6\text{in} \cdot 14\text{in}\)

\(\displaystyle A = 84\text{in}^2\)

Example Question #33 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

\(\displaystyle 36\text{in}^2\)

\(\displaystyle 96\text{in}^2\)

\(\displaystyle 24\text{in}^2\)

\(\displaystyle 48\text{in}^2\)

\(\displaystyle 56\text{in}^2\)

Correct answer:

\(\displaystyle 48\text{in}^2\)

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 8in.  We also know the height is 12in.  So, we can substitute.  We get

\(\displaystyle A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}\)

\(\displaystyle A = 4\text{in} \cdot 12\text{in}\)

\(\displaystyle A = 48\text{in}^2\)

Example Question #61 : Plane Geometry

Find the area of a triangle with a base of 10in and a height of 11in.

Possible Answers:

\(\displaystyle 110\text{in}^2\)

\(\displaystyle 58\text{in}^2\)

\(\displaystyle 21\text{in}^2\)

\(\displaystyle 42\text{in}^2\)

\(\displaystyle 55\text{in}^2\)

Correct answer:

\(\displaystyle 55\text{in}^2\)

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 10in.  We also know the height of the triangle is 11in.  So, we get

\(\displaystyle A = \frac{1}{2} \cdot 10\text{in} \cdot 11\text{in}\)

\(\displaystyle A = 5\text{in} \cdot 11\text{in}\)

\(\displaystyle A = 55\text{in}^2\)

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

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

\(\displaystyle 48\text{in}^2\)

\(\displaystyle 96\text{in}^2\)

\(\displaystyle 32\text{in}^2\)

\(\displaystyle 54\text{in}^2\)

\(\displaystyle 72\text{in}^2\)

Correct answer:

\(\displaystyle 48\text{in}^2\)

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 8in.  We also know the height of the triangle is 12in.

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

\(\displaystyle A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}\)

\(\displaystyle A = 4\text{in} \cdot 12\text{in}\)

\(\displaystyle A = 48\text{in}^2\)

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

Find the area of a triangle with a base of \(\displaystyle 7\textup{ cm}\) and a height of \(\displaystyle 12\textup{ cm}\).

Possible Answers:

\(\displaystyle 42\text{cm}\)

\(\displaystyle 84\text{cm}\)

\(\displaystyle 48\text{cm}^2\)

\(\displaystyle 42\text{cm}^2\)

\(\displaystyle 84\text{cm}^2\)

Correct answer:

\(\displaystyle 42\text{cm}^2\)

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.

 

We know the base is 7cm and the height is 12cm.  Knowing this, we will substitute into the formula.  We get

\(\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 7\text{cm} \cdot 12\text{cm}\)

\(\displaystyle \text{area of triangle} = \frac{1}{2} \cdot 84\text{cm}^2\)

\(\displaystyle \text{area of triangle} = \frac{1}{2} \cdot \frac{84\text{cm}^2}{1}\)

\(\displaystyle \text{area of triangle} = \frac{1 \cdot 84\text{cm}^2}{2 \cdot 1}\)

\(\displaystyle \text{area of triangle} = \frac{84\text{cm}^2}{2}\)

\(\displaystyle \text{area of triangle} = 42\text{cm}^2\)

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