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7th Grade Math : Geometry

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Example Question #1 : Geometry

If a rectangle possesses a width of $2\textup{ inches}$ $\displaystyle 2\textup{ inches}$ and has a perimeter of $18\textup{ inches}$ $\displaystyle 18\textup{ inches}$ , then what is the length?

Possible Answers:

$8\textup{ inches}$ $\displaystyle 8\textup{ inches}$

$7\textup{ inches}$ $\displaystyle 7\textup{ inches}$

$16\textup{ inches}$ $\displaystyle 16\textup{ inches}$

$14\textup{ inches}$ $\displaystyle 14\textup{ inches}$

Correct answer:

$7\textup{ inches}$ $\displaystyle 7\textup{ inches}$

Explanation:

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

P=2l+2w $\displaystyle P=2l+2w$

We can substitute in our known values and solve for our unknown variable (i.e. length):

$\displaystyle 18=2l+2(2)$

18=2l+4 $\displaystyle 18=2l+4$

We want to isolate the $\displaystyle l$ to one side of the equation. In order to do this, we will first subtract $\displaystyle 4$ from both sides of the equation.

$\frac{\begin{array}[b]{r}18=2l+4\\ -4\ \ \ \ \ \ -4\end{array}}{\\\\14=2l}$ $\displaystyle \frac{\begin{array}[b]{r}18=2l+4\\ -4\ \ \ \ \ \ -4\end{array}}{\\\\14=2l}$

Next, we can divide each side by $\displaystyle 2$

$\frac{\begin{array}[b]{r}\frac{14}{2}=\frac{2l}{2}\\\end{array}}{7=l}$ $\displaystyle \frac{\begin{array}[b]{r}\frac{14}{2}=\frac{2l}{2}\\\end{array}}{7=l}$

The length of the rectangle is $7\textup{ inches}$ $\displaystyle 7\textup{ inches}$

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Example Question #1 : Geometry

The figure represents a set of supplementary angles, solve for $\displaystyle x$ .

Possible Answers:

$83^\circ$ $\displaystyle 83^\circ$

$81^\circ$ $\displaystyle 81^\circ$

$84^\circ$ $\displaystyle 84^\circ$

$82^\circ$ $\displaystyle 82^\circ$

Correct answer:

$81^\circ$ $\displaystyle 81^\circ$

Explanation:

Supplementary angles are defined as two angles that when added together equal $180^\circ$ $\displaystyle 180^\circ$

From the question, we know that the two angles are supplementary, and thus equal $180^\circ$ $\displaystyle 180^\circ$ , so we can set up the following equation:

$\displaystyle x+99=180$

Next we can solve for $\displaystyle x$ :

$\frac{\begin{array}[b]{r}x+99=180\\ -99\ \ -99\end{array}}{x= 81}$ $\displaystyle \frac{\begin{array}[b]{r}x+99=180\\ -99\ \ -99\end{array}}{x= 81}$

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Example Question #3 : Geometry

What is the area of the circle provided?

Possible Answers:

$400\pi\textup{ in}^2$ $\displaystyle 400\pi\textup{ in}^2$

$1\textup,600\pi\textup{ in}^2$

$1\textup,400\pi\textup{ in}^2$

$40\pi\textup{ in}^2$ $\displaystyle 40\pi\textup{ in}^2$

Correct answer:

$400\pi\textup{ in}^2$ $\displaystyle 400\pi\textup{ in}^2$

Explanation:

In order to solve this problem, we need to recall the formula for the area of a circle:

$A= r^2\pi$ $\displaystyle A= r^2\pi$

The circle in this question provides us with the diameter, so we first have to solve for the radius. Remember, the radius is half the diameter:

$r=\frac{d}{2}$ $\displaystyle r=\frac{d}{2}$

$r=\frac{40}{2}$ $\displaystyle r=\frac{40}{2}$

r=20 $\displaystyle r=20$

Now that we have the radius we can use the formula to solve:

$A=20^2\pi$ $\displaystyle A=20^2\pi$

Solve:

$A=400\pi\textup{ in}^2$ $\displaystyle A=400\pi\textup{ in}^2$

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Example Question #4 : Geometry

6 8 10

What is the area of the triangle pictured above?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is calculated using the formula $Area = \frac{1}{2}(Base\times Height)$ $\displaystyle Area = \frac{1}{2}(Base\times Height)$ . Importantly, the height is a perpendicular line between the base and the opposite point. In a right triangle like this one, you're in luck: the triangle as drawn already has that perpendicular line as one of the two sides. So here we will calculate $\frac{1}{2}(8\times 6)$ $\displaystyle \frac{1}{2}(8\times 6)$ . That gives us an answer of 24.

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7th Grade Math : Geometry

Study concepts, example questions & explanations for 7th Grade Math

All 7th Grade Math Resources

Example Questions

Example Question #1 : Geometry

Example Question #1 : Geometry

Example Question #3 : Geometry

Example Question #4 : Geometry

All 7th Grade Math Resources

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