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ISEE Lower Level Math : Triangles

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Example Question #311 : Plane Geometry

Find the area of a triangle with a base of 7in and a height that is two times the base.

Possible Answers:

$98\text{in}^2$

$56\text{in}^2$

$49\text{in}^2$

$78\text{in}^2$

$36\text{in}^2$

Correct answer:

$49\text{in}^2$

Explanation:

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

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

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

Now, we know the base of the triangle is 7in. We also know the height is two times the base. Therefore, the height is 14in.

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

$A = \frac{1}{2} \cdot 7\text{in} \cdot 14\text{in}$

$A = 7\text{in} \cdot 7\text{in}$

$A = 49\text{in}^2$

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Example Question #312 : Plane Geometry

Find the area of a triangle with the following measurements:

height: 5in
base: 6in

Possible Answers:

$15\text{in}^2$

$17\text{in}^2$

$16\text{in}^2$

$11\text{in}^2$

$30\text{in}^2$

Correct answer:

$15\text{in}^2$

Explanation:

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

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

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

Now, we know the base of the triangle is 6in. We also know the height of the triangle is 5in. So, we get

$A = \frac{1}{2} \cdot 6\text{in} \cdot 5\text{in}$

$A = 3\text{in} \cdot 5\text{in}$

$A = 15\text{in}^2$

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Example Question #313 : Plane Geometry

Use the following triangle to answer the question:

Triangle5

If the triangle has a height of $9\textup{ ft}$ , find the area.

Possible Answers:

$20\textup{ ft}^2$

$21\textup{ ft}^2$

$17\textup{ ft}^2$

$26\textup{ ft}^2$

$18\textup{ ft}^2$

Correct answer:

$18\textup{ ft}^2$

Explanation:

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

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

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

Now, given the triangle

Triangle5

we can see the base is 4ft. We also know it has a height of 9ft.

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

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 9\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 36\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{36\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 36\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{36\text{ft}^2}{2}$

$\text{area of triangle} = 18\text{ft}^2$

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

The triangle below has a perimeter of $32 \textup{ cm}$ . The lengths of two sides are shown below.

What is the length of the third side?

Possible Answers:

$12 \textup{ cm}$

$23 \textup{ cm}$

$11 \textup{ cm}$

$48 \textup{ cm}$

Correct answer:

$11 \textup{ cm}$

Explanation:

Remember, the perimeter of a triangle is the sum of its three sides. First, sum up the two side lengths that we are given in the question:

$9 \textup{ cm}+12 \textup{ cm}=21 \textup{ cm}$

To find the third side, subtract the sides we know from the total perimeter:

$32 \textup{ cm}-21 \textup{ cm}=\textbf{11 \textup{cm}}$

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

An equilateral triangle has a perimeter of $18\; in$ . How long is each side?

Possible Answers:

$3\; in$

$7\; in$

$9\; in$

$6\; in$

$8\; in$

Correct answer:

$6\; in$

Explanation:

An equilateral triangle has three congruent sides, i.e. the sides are all the same length.

The perimeter of an equilateral triangle is given by P=3s .

Thus, P=3s=18 ; then divide each side by three to get $s=6\; in$ .

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Example Question #341 : Geometry

Use the triangle to answer the question.

Triangle_perimeter_2

What is the perimeter of the triangle?

Possible Answers:

46cm

98cm

24cm

32 cm

Correct answer:

32 cm

Explanation:

To find the perimeter, add all the sides together.

$11 \textup{ cm}+13\textup{ cm}+8\textup{ cm}=32\textup{ cm}$

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

An equilateral triangle has a side length equal to 4cm .

What is the perimeter of the triangle?

Possible Answers:

18cm

16cm

12cm

24cm

8cm

Correct answer:

12cm

Explanation:

Because it is an equilateral triangle, all sides have the same length (4cm) .

The perimeter is the sum of the length of the sides.

$P=s+s+s=4\: cm+4\: cm+4\: cm=12\: cm$

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

Set_3b

Figure not drawn to scale

The perimeter of isosceles triangle $\bigtriangleup ABC$ is 25in .

If $\overline{AB}$ and $\overline{BC}$ are equal to each other and $\overline{AC}$ is 5in , what is the length of $\overline{AB}$ ?

Possible Answers:

$5\ in$

$20\ in$

$10\ in$

$15\ in$

$8\ in$

Correct answer:

$10\ in$

Explanation:

The perimeter of the triangle is equal to the sum of the lengths of all the sides.

$\overline{AB}+\overline{BC}+\overline{AC}= Perimeter$

$\overline{AB}+\overline{BC}+\5= 25$

Because the triangle is an isosceles triangle, the triangle has two equal sides, which we know are $\overline{AB}$ and $\overline{BC}$ .

Since $2*\overline{AB}$ is the same as $\overline{AB}+\overline{BC}$ , we can say: $2*\overline{AB}+5= 25$ .

We now solve for $\overline{AB}$ :

$2*\overline{AB}+5= 25$ Subtract from both sides

$2*\overline{AB}= 20$

$\frac{2}{2}*\overline{AB}= \frac{20}{2}$ Divide both sides by

$\overline{AB}=10$

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

What is the name of the longest side of a right triangle?

Possible Answers:

Obtuse

Equilateral

Length

Base

Hypotenuse

Correct answer:

Hypotenuse

Explanation:

The hypotenuse is the longest side of a triangle with a right angle.

All the other terms refer to something else. Obtuse refers to an angle over 90 degrees. Length is too general of a term, and refers to the measurement of any given side. Equilateral refers to a triangle in which all angles and side are of equal measurement. Base refers to the side that is perpendicular to the measure of the height, meaning that it will be one of the shorter sides.

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

In an isosceles triangle, two side are 4 feet long. Which of the following is NOT a possible length of the third side?

Possible Answers:

8 feet

1 foot

7 feet

2.5 feet

5 feet

Correct answer:

8 feet

Explanation:

For triangles, it is impossible for a third side to be equal to or greater than the sum of the two other sides.

Given that the sum of the two sides of this triangle is 8, it is impossible for the third side to be equal to 8 feet.

$\text{side}<4+4$

$\text{side}<8$

$8\nless8$

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ISEE Lower Level Math : Triangles

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

All ISEE Lower Level Math Resources

Example Questions

Example Question #311 : Plane Geometry

Example Question #312 : Plane Geometry

Example Question #313 : Plane Geometry

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

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

Example Question #341 : Geometry

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

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

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

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

All ISEE Lower Level Math Resources

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