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docker41 [41]
3 years ago
15

What is the area of the figure:

Mathematics
2 answers:
Luba_88 [7]3 years ago
6 0

For this case we have that the area of the triangle is given by:

A = \frac {b * h} {2}

Where:

b: It's the base

h: It's the height

We have to:

cos (45) = \frac {b} {24}\\b = 24 * cos (45)\\b = \frac {\sqrt {2}} {2} * 24\\b = 12 \sqrt {2}

The atura will be given by:

sin (45) = \frac {h} {24}\\h = 24 * sin (45)\\h = \frac {\sqrt {2}} {2} * 24\\h = 12 \sqrt {2}

So, the area is:

A = \frac {12 \sqrt {2} * 12 \sqrt {2}} {2}\\A=\frac{(12\sqrt{2})^2}{2}\\A = 144

Answer:

144

viktelen [127]3 years ago
4 0

Answer:

Area=144

Step-by-step explanation:

In right triangle ABC,

\sin\left(45^o\right)=\frac{BC}{AB}

\frac{1}{\sqrt{2}}=\frac{BC}{24}

\frac{1}{\sqrt{2}}=\frac{Height}{24}

\frac{24}{\sqrt{2}}=Height

Height=\frac{24}{\sqrt{2}}

similarly

\cos\left(45^o\right)=\frac{AC}{AB}

\frac{1}{\sqrt{2}}=\frac{AC}{24}

\frac{1}{\sqrt{2}}=\frac{Base}{24}

\frac{24}{\sqrt{2}}=Base

Base=\frac{24}{\sqrt{2}}

Then area of right triangle =\frac{1}{2}\left(Base\right)\left(Height\right)

=\frac{1}{2}\left(\frac{24}{\sqrt{2}}\right)\left(\frac{24}{\sqrt{2}}\right)

=\frac{576}{4}=144

Hence Area=144

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