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GED Math : Perimeter and Sides of Quadrilaterals

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Example Question #41 : Perimeter And Sides Of Quadrilaterals

A square and a right triangle share a side as shown by the figure below.

Find the area of the square.

Possible Answers:

169

144

196

Correct answer:

169

Explanation:

Notice that the side of the square is the same as the hypotenuse of the right triangle.

Use Pythagorean's theorem to find the length of the hypotenuse.

$\text{Hypotenuse}=\sqrt{5^2+12^2}=\sqrt{169}=13$

Now that we have the length of a side of the square, find the area.

$\text{Area of Square}=13^2=169$

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Example Question #42 : Perimeter And Sides Of Quadrilaterals

Find the perimeter of trapezoid ABCD if $\measuredangle ADC=60^{\circ}$ .

Possible Answers:

$18+3\sqrt{3}$

$12+12\sqrt{3}$

$16+\sqrt{3}$

$16+12\sqrt{3}$

Correct answer:

$16+12\sqrt{3}$

Explanation:

Since we know that $\measuredangle ADC=60^{\circ}$ , we can set up the following ratio to find the lengths of and because of the 30-60-90 triangle.

$\frac{6}{\sqrt3}=\frac{DE}{1}$

$DE=\frac{6}{\sqrt3}=2\sqrt{3}$

Using that value,

$\frac{2\sqrt3}{1}=\frac{AD}{2}$

$AD=4\sqrt{3}$

Thus, we can find the perimeter of the trapezoid.

$\text{Perimeter}=8+4\sqrt{3}+2\sqrt{3}+8+2\sqrt{3}+4\sqrt{3}=16+12\sqrt{3}$

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Example Question #43 : Perimeter And Sides Of Quadrilaterals

What is the perimeter of a square that has an area of $169ft^{2}$ ?

Possible Answers:

$42.25ft^{2}$

26ft

$52ft^{2}$

52ft

13ft

Correct answer:

52ft

Explanation:

First we need to recognize that in order to find perimeter we first need to figure out the length of each side of the square. The formula for area of a square is

$Area=s^{2}$

where is side

$169ft^{2}=s^{2}$

To solve for we need to take the square root of both sides

$\sqrt{169ft^{2}}=\sqrt{s^{2}}$

13ft=s

Now that we know our side length is 13, we can plug it into our perimeter equation and solve for s

$Perimeter=4\cdot s$

Perimeter=4 (13ft)

We multiply 4 and 13

Perimeter=52ft

Notice our answer is in ft because perimeters are linear

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GED Math : Perimeter and Sides of Quadrilaterals

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #41 : Perimeter And Sides Of Quadrilaterals

Example Question #42 : Perimeter And Sides Of Quadrilaterals

Example Question #43 : Perimeter And Sides Of Quadrilaterals

All GED Math Resources

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