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

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Example Questions

Example Question #2042 : Hspt Mathematics

The three angles of a triangle are labeled , , and . If is $97^{\circ}$ , what is the value of X+Y ?

Possible Answers:

$83^{\circ}$

$73^{\circ}$

$93^{\circ}$

$17^{\circ}$

Correct answer:

$83^{\circ}$

Explanation:

Given that the three angles of a triangle always add up to 180 degrees, the following equation can be used:

X+Y+Z=180

X+Y+97=180

X+Y=83

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Example Question #42 : Plane Geometry

In an equilateral triangle, which of the following is NOT true?

Possible Answers:

There is a 60 degree angle

All angles are equal

There is a 90 degree angle

All sides are equal

Correct answer:

There is a 90 degree angle

Explanation:

In an equilateral triangle, all sides and angles are equal. All the angles equal 60 degrees, so there is a 60 degree angle.

Therefore, the answer choice, “There is a 90 degree angle” is not true and is the correct answer choice.

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Example Question #241 : Ssat Middle Level Quantitative (Math)

The hypotenuse of a right triangle is feet; it has one leg feet long. Give its area in square inches.

Possible Answers:

$101,088 \textrm{ in}^{2}$

$42,120 \textrm{ in}^{2}$

$43,120 \textrm{ in}^{2}$

$77,760 \textrm{ in}^{2}$

$38,880 \textrm{ in}^{2}$

Correct answer:

$38,880 \textrm{ in}^{2}$

Explanation:

The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set c = 39 , b = 36 :

$a^{2} = c^{2} - b^{2}$

$a^{2} = 39 ^{2} - 36^{2}$

$a^{2} = 1,521 - 1,296$

$a^{2} = 225$

$a = \sqrt{225} = 15$

The legs have length and feet; multiply both dimensions by to convert to inches:

$15 \times 12 = 180$ inches

$36 \times 12 = 432$ inches.

Now find half the product:

$A = \frac{1}{2} \cdot 180 \cdot 432 = 38,880\ in^{2}$

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Example Question #242 : Ssat Middle Level Quantitative (Math)

What is the area (in square feet) of a triangle with a base of feet and a height of feet?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is found by multiplying the base times the height, divided by .

$Area =\frac{base\cdot height}{2}$

$Area =\frac{4\cdot 7}{2}$

Area=14

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Example Question #23 : Area Of A Triangle

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

Possible Answers:

Correct answer:

Explanation:

The formula for the area of a triangle is $\dpi{100} Area=\frac{1}{2}\times base\times height$ .

Plug the given values into the formula to solve:

$\dpi{100} Area=\frac{1}{2}\times 12\times 3$

$\dpi{100} Area=\frac{1}{2}\times 36$

$\dpi{100} Area=18$

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Example Question #41 : Triangles

You have two traingular gardens next to each other. They both have a base of and a height of . What is the total area?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is

$\frac{1}{2}*base*height$

and since there are two identical traingles, them put together will just be

base*height .

So your answer will just be 5*7=35 .

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Example Question #45 : Plane Geometry

Pentagon

The above figure depicts Square ABCD with perimeter 240. , , and are the midpoints of $\overline{AD}$ , $\overline{BC}$ , and $\overline{AB}$ , respectively.

Give the area of Polygon XZYCD .

Possible Answers:

2,700

3,600

3,150

1,800

Correct answer:

2,700

Explanation:

Square ABCD has perimeter 240, so the length of each side is one fourth of this, or

$\frac{1}{4} \cdot 240 = 60$ .

Segment $\overline{XY}$ , as seen below, divides Polygon CDXZY into two figures:

Pentagon 1

One figure is $\bigtriangleup XZY$ , with base and height 60 and 30, respectively. Its area is half their product, or

$A_{1} = \frac{1}{2} \cdot 60 \cdot 30 = 900$

The other figure is Rect XYCD , whose length and width are 60 and 30, respectively. Its area is their product, or

$A_{2} = \cdot 60 \cdot 30 = 1,800$

Add these areas:

$A_{1} +A_{2} = 900 + 1,800 = 2,700$ .

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Example Question #51 : Triangles

Right triangle 3

Give the area of the above triangle.

Possible Answers:

1,625

812 .5

750

1,500

Correct answer:

750

Explanation:

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

$A = \frac{1}{2} \cdot 25 \cdot 60 = 750$

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Example Question #52 : Triangles

Find the area of a triangle with a base of 10cm and a height that is half the base.

Possible Answers:

$25\text{cm}^2$

$50\text{cm}^2$

$25\text{cm}$

$20\text{cm}$

$50\text{cm}$

Correct answer:

$25\text{cm}^2$

Explanation:

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

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

Now, we know the base has a length of 10cm. We also know the height is half the base. Therefore, the height is 5cm. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 10\text{cm} \cdot 5\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 50\text{cm}^2$

$\text{area of triangle} = 25\text{cm}^2$

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Example Question #52 : Triangles

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

Possible Answers:

125m^2

2500m^2

1250m^2

250m^2

Correct answer:

1250m^2

Explanation:

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

To find the area of a triangle, use the following:

$A_{triangle}=\frac{1}{2}bh$

Where b and h are the base and height.

In this case, we are told that the base and height are both 50 meters, thus, the perimeter will be:

$A_{triangle}=\frac{1}{2}50m*50m=\frac{1}{2}*2500m^2=1250m^2$

So our answer is:

1250m^2

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

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #2042 : Hspt Mathematics

Example Question #42 : Plane Geometry

Example Question #241 : Ssat Middle Level Quantitative (Math)

Example Question #242 : Ssat Middle Level Quantitative (Math)

Example Question #23 : Area Of A Triangle

Example Question #41 : Triangles

Example Question #45 : Plane Geometry

Example Question #51 : Triangles

Example Question #52 : Triangles

Example Question #52 : Triangles

All ISEE Middle Level Math Resources

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