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GED Math : Triangles

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Example Questions

Example Question #23 : Area Of A Triangle

What is the area of a triangle with a base of 8 and a height of 30?

Possible Answers:

120

240

Correct answer:

120

Explanation:

Write the formula for the area of a triangle.

$A =\frac{bh}{2}$

Substitute the dimensions.

$A =\frac{8(30)}{2} = 4(30) = 120$

The answer is: 120

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Example Question #24 : Area Of A Triangle

Find the area of a triangle with a base of 100 and a height of 300.

Possible Answers:

12000

30000

15000

24000

18000

Correct answer:

15000

Explanation:

Write the formula for the area of a triangle.

$A = \frac{bh}{2}$

Substitute the base and the height into the equation.

$A = \frac{(100)(300)}{2} = 100(150 ) = 15000$

The answer is: 15000

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Example Question #53 : Triangles

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, how much area will the garden take up?

Possible Answers:

48ft^2

12ft^2

14ft^2

24ft^2

Correct answer:

24ft^2

Explanation:

You want to build a garden in the shape of a right triangle. If the two arms will be 6ft and 8ft, how much area will the garden take up?

To find the area of a triangle, use the following formula.

$A=\frac{1}{2}bh$

Note that in a right triangle, our two arms correspond to our base and our height. Furthermore, it does not matter which is which, because when we multiply, order does not matter.

So, to find our area, simply plug in and simplify.

$A=\frac{1}{2}(6ft)(8ft)=\frac{1}{2}(48ft^2)=24ft^2$

So, our answer is 24 ft squared

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Example Question #54 : Triangles

What is the area of an equilateral triangle that has a perimeter of ? Round your answer to the nearest hundredths place.

Possible Answers:

85.20

73.18

79.88

29.10

Correct answer:

73.18

Explanation:

Start by finding the length of a side of the triangle.

$\text{side}=\frac{\text{Perimeter}}{3}$

$\text{side}=\frac{39}{3}=13$

Next, recall how to find the area of an equilateral triangle.

$\text{Area}=\frac{\sqrt3}{4}\text{side}^2$

Plug in the length of the side to find the area.

$\text{Area}=\frac{\sqrt3}{4}(13)^2=\frac{\sqrt3}{4}(169)=73.18$

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Example Question #231 : 2 Dimensional Geometry

If the height of a triangle is twice the length of the base, and the base length is 3.5 inches, what is the area of the triangle?

Possible Answers:

$12.25 in^{2}$

$15in^{2}$

$24.5in^{2}$

$6.125in^{2}$

12.25in

Correct answer:

$12.25 in^{2}$

Explanation:

First we need to know that the formula for area of a triangle:

$Area= \frac{1}{2}(Base\cdot Height)$

We know that our base is 3.5 inches, and our height is twice that, which is 7 in.

Now we can plug in our base and height to the equation

$Area=\frac{1}{2}(3.5 in\cdot 7 in)$

Multiply and solve

$Area=\frac{1}{2}(24.5in^{2})$

$Area=12.25in^{2}$

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Example Question #232 : 2 Dimensional Geometry

What is the area of a triangle with a height that is three times the length of the base, if the base is 4cm?

Possible Answers:

$28cm^{2}$

48cm

$24cm^{2}$

24cm

$48cm^{2}$

Correct answer:

$24cm^{2}$

Explanation:

First we need to recall the formula for area of a triangle:

$Area=\frac{1}{2}(base\cdot height)$

We know that our base is 4cm, and our height is 3 times the length of the base, since 4x3=12 we know that our height is 12cm

Now we can plug in our numbers

$Area=\frac{1}{2}(4cm\cdot 12cm)$

First we multiply 4 and 12

$Area=\frac{1}{2}(48cm^{2})$

Next we distribute the fraction which is the same as dividing in half

$Area=24cm^{2}$

Notice our answer is in centimeters since we multiplied two terms measured in centimeters

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Example Question #1 : Angles And Triangles

Which of the following can be the measures of the three angles of an acute isosceles triangle?

Possible Answers:

$32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$

$50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$

$80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$

$45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

Correct answer:

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$

Explanation:

For the triangle to be acute, all three angles must measure less than $90 ^{\circ }$ . We can eliminate $32 ^{\circ }, 32 ^{\circ }, 116^{\circ }$ and $45 ^{\circ }, 45 ^{\circ }, 90^{\circ }$ for this reason.

In an isosceles triangle, at least two angles are congruent, so we can eliminate $50 ^{\circ }, 60 ^{\circ }, 70 ^{\circ }$ .

The degree measures of the three angles of a triangle must total 180, so, since $80 ^{\circ }+ 80 ^{\circ }+ 40 ^{\circ } = 200^{\circ }$ , we can eliminate $80 ^{\circ }, 80 ^{\circ }, 40 ^{\circ }$ .

$36^{\circ }, 72 ^{\circ }, 72 ^{\circ }$ is correct.

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Example Question #2 : Angles And Triangles

Triangle

Note: Figure NOT drawn to scale.

Refer to the above triangle. Evaluate .

Possible Answers:

x = 31

x = 63

x = 39

x = 51

Correct answer:

x = 39

Explanation:

The degree measures of a triangle total $180^{\circ }$ , so

x + (x+24) + 2x = 180

4x+24 = 180

4x+24 -24 = 180 -24

4x = 156

$4x \div 4 = 156 \div 4$

x = 39

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Example Question #55 : Triangles

Triangle

Note: Figure NOT drawn to scale.

Refer to the above figure. Evaluate .

Possible Answers:

$y = 20 \frac{1}{2}$

y = 31

y = 41

$y = 56 \frac{1}{2}$

Correct answer:

$y = 56 \frac{1}{2}$

Explanation:

The degree measures of the interior angles of a triangle total $180 ^{\circ }$ , so, if we let $x^{\circ }$ be the measure of the unmarked angle, then

x + 41 + 72 = 180

x + 113 = 180

x = 67

Three angles with measures $67^{\circ}, y^{\circ}, y^{\circ}$ together form a straight angle, so

y+ y + 67= 180

2y+ 67= 180

2y+ 67- 67 = 180 - 67

2y = 113

$2y \div 2 = 113 \div 2$

$y = 56 \frac{1}{2}$

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Example Question #3 : Angles And Triangles

Thingy

Figure drawn to scale.

Refer to the above diagram.

Which of the following is a valid description of $\Delta EFC$ ?

Possible Answers:

Equiangular

Right

Obtuse

Acute

Correct answer:

Obtuse

Explanation:

One of the angles of $\Delta EFC$ - namely, $\angle EFC$ - can be seen to be an obtuse angle, as it is wider than a right angle. This makes $\Delta EFC$ , by definition, an obtuse triangle.

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GED Math : Triangles

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #23 : Area Of A Triangle

Example Question #24 : Area Of A Triangle

Example Question #53 : Triangles

Example Question #54 : Triangles

Example Question #231 : 2 Dimensional Geometry

Example Question #232 : 2 Dimensional Geometry

Example Question #1 : Angles And Triangles

Example Question #2 : Angles And Triangles

Example Question #55 : Triangles

Example Question #3 : Angles And Triangles

All GED Math Resources

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