All categories

3 years ago

The coordinates for a rectangle are (3,10) (9,10) (9,6) and (3,6). What is the area

Mathematics

2 answers:

GalinKa [24]3 years ago

6 0

Check the picture below. You can pretty much count the units off the grid for its width and length.

andreev551 [17]3 years ago

4 0

Hello!

First of all, let's look at the horizontal points, (3,6) and (3,10) since they y-axis is 10 and 6, we subtract and get 4 as one side length.

We do the same for the vertical points. The distance between (3,10) and (9,10) is 6 units, so 6 is our other side length.

Now we multiply.

4(6)=24

Therefore the area is 24 square units.

I hope this helps!

You might be interested in

Which function shows the combined cost in dollars, y, for three shipments with x number of chargers and tablets?

ANEK [815]

Answer:

the answer is b

Step-by-step explanation:

7 0

4 years ago

Will give brainliest if correct

Nuetrik [128]

Answer:

Step-by-step explanation:

$|\angle AEC|=(4x)^o \quad\implies\quad |\angle AED|=180^o-(4x)^o\\\\\\\widehat{AC}=120^o\quad\implies\quad |\angle AOC|=120^o\\\\|\angle AOC|=120^o \quad\implies\quad |\angle ADC|=\frac12\cdot120^o=60^o\\\\\\\widehat{BD}=(2x)^o\quad\implies\quad |\angle BOD|=(2x)^o\\\\|\angle BOD|=(2x)^o \quad\implies\quad |\angle ADC|=\frac12\cdot(2x)^o=x^o\\\\\\ \Delta ADE:\\\\180^o-(4x)^o+60^o+x^o=180^o\\\\-(3x)^o=-60^o\\\\x=20^o\\\\\\|\angle AED|=180^o-4\cdot20^o=100^o$

6 0

3 years ago

Consider the right cone and right triangular prism below. Suppose that all measurements are labeled in centimeters.

Musya8 [376]

Answer:

The prism has a volume about 340 cubic centimeters larger than the cone.

Step-by-step explanation:

<u />

<u>Formulas</u>

$\sf Surface\:area\:of\:a\:cone=\pi r \left(r+\sqrt{h^2+r^2}\right)$

$\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2 h$

where:

r = radius of circular base
h = height perpendicular to the base

Given:

r = 3 cm
h = 6 cm

Substitute the given values into the formulas:

$\begin{aligned}\sf Surface\:area\:of\:cone & =\pi (3) \left(3+\sqrt{6^2+3^2}\right)\\ & = 3 \pi \left (3+\sqrt{36+9}\right)\\ & = 3\pi (3+\sqrt{45})\\ & = 3\pi(3+3\sqrt{5})\\ & = 91.5 \:\: \sf cm^2\:(1\:d.p.)\end{aligned}$

$\begin{aligned}\textsf{Volume of cone} & =\dfrac{1}{3} \pi (3)^2 (6)\\& = \dfrac{54}{3} \pi \\ & = 18 \pi \\ & = 56.5\:\: \sf cm^3 \:(1 \: d.p.)\end{aligned}$

<h3><u>Prism</u></h3>

<u>Formulas</u>

<u /> $\textsf{Surface area of a prism}=\textsf{Total area of all the sides}$

$\textsf{Volume of a prism}=\sf \textsf{Area of base} \times height$

$\textsf{Area of a triangle}=\sf \dfrac{1}{2} \times base \times height$

$\textsf{Area of a rectangle}=\sf width \times length$

Given:

Height of triangular base = 10 cm
Base of triangular base = 8 cm
Height of prism = 10 cm

Find the <u>area of the triangular base</u> of the prism:

$\begin{aligned}\textsf{Area of the base} & = \dfrac{1}{2} \times 8 \times 10\\& = 40\:\: \sf cm^2\end{aligned}$

Find the third edge of the triangular base by using <u>Pythagoras Theorem</u>:

$\begin{aligned}a^2+b^2 & = c^2\\\implies 8^2+10^2 & = c^2\\164 & = c^2\\c & = \sqrt{164}\\c & = 2\sqrt{41}\end{aligned}$

Use the found values and the formulas to find the surface area of volume of the prism:

$\begin{aligned}\textsf{Surface area of prism} & = \sf 2\:triangles+3\:rectangles\\& = 2\left(40\right) + (10 \times 10)+(10 \times 8)+ (10 \times 2\sqrt{41})\\& = 80 + 100 + 80 + 20\sqrt{41}\\& = 388.1 \:\: \sf cm^2\:(1\:d.p.)\end{aligned}$