Math - Plane Geometry | Practice Hub

In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?

2√5

10√2

6√2

Explanation

Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated. 102+102=c2. 200=c2. √200=c. √100√2=c. 10√2=c

What is the hypotenuse of a right triangle with side lengths and ?

Explanation

The Pythagorean Theorem states that . This question gives us the values of and , and asks us to solve for .

Take and and plug them into the equation as and :

$12^{2}+16^{2}=c^{2}$

Now we can start solving for :

$144+256=c^{2}$

$400=c^{2}$

$\sqrt{400}=\sqrt{c^{2}}$

The length of the hypotenuse is .

What is the height of an equilateral triangle with side 6?

$3\sqrt{3}$

$6\sqrt{2}$

Explanation

When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. Because of that relationship, the height (which is across from the $60^{\circ}$ ) is $3\sqrt{3}$ .

To the nearest tenth, give the area of a circle with diameter $7 \frac{1}{2}$ inches.

$44.2 \textrm{ in}^{2}$

$88.4 \textrm{ in}^{2}$

$22.1 \textrm{ in}^{2}$

$176.7 \textrm{ in}^{2}$

$56.3 \textrm{ in}^{2}$

Explanation

The radius of a circle with diameter $7 \frac{1}{2}$ inches is half that, or $3 \frac{3}{4} = 3.75$ inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 3.75^{2} \approx 44.2 \textrm{ in}^{2}$

2√5

10√2

6√2

Explanation

To the nearest tenth, give the area of a circle with diameter $7 \frac{1}{2}$ inches.

$44.2 \textrm{ in}^{2}$

$88.4 \textrm{ in}^{2}$

$22.1 \textrm{ in}^{2}$

$176.7 \textrm{ in}^{2}$

$56.3 \textrm{ in}^{2}$

Explanation

The radius of a circle with diameter $7 \frac{1}{2}$ inches is half that, or $3 \frac{3}{4} = 3.75$ inches. The area of the circle is

$A = \pi r^{2} = \pi \cdot 3.75^{2} \approx 44.2 \textrm{ in}^{2}$

Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

Circle_graph_area3

100_π_

50_π_

25_π_

10_π_

20_π_

Explanation

Circle_graph_area2

What is the hypotenuse of a right triangle with side lengths and ?

Explanation

The Pythagorean Theorem states that . This question gives us the values of and , and asks us to solve for .

Take and and plug them into the equation as and :

$12^{2}+16^{2}=c^{2}$

Now we can start solving for :

$144+256=c^{2}$

$400=c^{2}$

$\sqrt{400}=\sqrt{c^{2}}$

The length of the hypotenuse is .

This figure is a regular hexagon with one side measuring 6 cm. Hexagon

What is the perimeter of the regular hexagon in centimeters?

Explanation

The perimeter of a regular hexagon is just the sum of all 6 sides. Because it's a regular hexagon, the perimemter is just six times one side (6 cm) or 36 cm.

Plane Geometry

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation