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What is the area of the figure:

What is the area of the figure:-example-1
User Clay Banks
by
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2 Answers

4 votes

Answer:

Area=144

Explanation:

In right triangle ABC,


\sin\left(45^o\right)=(BC)/(AB)


(1)/(√(2))=(BC)/(24)


(1)/(√(2))=(Height)/(24)


(24)/(√(2))=Height


Height=(24)/(√(2))

similarly


\cos\left(45^o\right)=(AC)/(AB)


(1)/(√(2))=(AC)/(24)


(1)/(√(2))=(Base)/(24)


(24)/(√(2))=Base


Base=(24)/(√(2))

Then area of right triangle
=(1)/(2)\left(Base\right)\left(Height\right)


=(1)/(2)\left((24)/(√(2))\right)\left((24)/(√(2))\right)


=(576)/(4)=144

Hence Area=144

User Madison
by
7.7k points
1 vote

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=((12√(2))^2)/(2)\\A = 144

Answer:

144

User Xis
by
7.7k points

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