How to find the area of this figure

Mathematics

1 answer:

stiv31 [10]3 years ago

3 0

Answer:

45 square units.

Step-by-step explanation:

Applying the pythagoras theorem:

Base of the bigger triangle = $\sqrt{15^2 - 9^2}$ = $\sqrt{144}$ = 12 units

Area of a triangle is given by $\frac{1}{2}$ × base × height

The area of the bigger triangle is $\frac{1}{2}$ × 12 × 9 = 54 square units.

The area of the smallest triangle is $\frac{1}{2}$ × (12 - 10) × 9 = 9 square units.

The area of the figure( required triangle) is 54 - 9 = 45 square units.

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What is the perimeter of the trapezoid with vertices Q(8, 8), R(14, 16), S(20, 16), and T(22, 8)? Round to the nearest hundredth

EleoNora [17]

Check the picture below.

so... you can pretty much see how long RS and QT are, you can just count the units off the grid.

now, let's find QR's length

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ 8 &,& 8~) 
% (c,d)
&R&(~ 14 &,& 16~)
\end{array}~~ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
QR=\sqrt{(14-8)^2+(16-8)^2}\implies QR=\sqrt{6^2+8^2}
\\\\\\
QR=\sqrt{36+64}\implies QR=\sqrt{100}\implies QR=10$

and let's also find the length for ST

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ 20 &,& 16~) 
% (c,d)
&T&(~ 22 &,& 8~)
\end{array}~ 
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{(22-20)^2+(8-16)^2}\implies ST=\sqrt{2^2+(-8)^2}
\\\\\\
ST=\sqrt{4+64}\implies ST=\sqrt{68}\implies ST=\sqrt{4\cdot 17}
\\\\\\
ST=\sqrt{2^2\cdot 17}\implies ST=2\sqrt{17}$

so, add the lengths of all sides, and that's the perimeter of the trapezoid.