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2 years ago

What is the area of the composite figure

Mathematics

1 answer:

kati45 [8]2 years ago

8 0

To solve this we will divide the given composite figure into three figures. The three figures will be 2 squares and 1 rectangle. Let's find their areas and add them!

$\boxed{ \sf \: area \: of \: square =side ^{2} }$

Side 3 metre

$\rm \implies \: area = 3 ^{2}$

$\rm \implies9$

<em>Thus, The area of 1st square is 9m²...</em>

The area of second square will be also 9m², because the sides of both squares are equal.

<h3>Now area of the reactangle⤵️</h3>

Length = 6m
Breadth = 7+3=10m

$\sf \: area \: of \: rectangle = length \times breadtg$

$\tt \dashrightarrow \: area = 10 \times 3$

$\tt \dashrightarrow \: area = 30m ^{2}$

<em>Thus, The area of rectangle is 30m²....</em>

Now, Add area of all the figures to get the total area.

$\bf \:total \: area = 9 + 9 + 30 \\ \bf= 48m {}^{2}$

<h3><em>Therefore, The total area of the composite figure is 48m²...~</em></h3>

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3 years ago

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Answer:

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Step-by-step explanation:

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4 years ago

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

8 0

3 years ago