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dem82 [27]
3 years ago
5

What is the area of the figure? Make sure to show your work and provide complete geometric explanations.

Mathematics
2 answers:
uysha [10]3 years ago
8 0

Answer:

A = 144\ ft

Step-by-step explanation:

The area of a triangle is:

A = 0.5b*h

Where b is the base of the triangle and h is the height

In this case we know the hypotenuse of the triangle and the angle B.

Then we can use the sine of the angle to find the side opposite the angle

By definition we know that

sin (\theta) = \frac{opposite}{hypotenuse}

In this case hypotenuse = 24

opposite = b

Then:

sin (45) = \frac{b}{24}

b= 24*sin(45)

b=12\sqrt{2}

Now

cos(\theta) = \frac{adjacent}{hypotenuse}

adjacent = a = h

cos(45) = \frac{h}{24}

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

Then the area is:

A = 0.5*12\sqrt{2}(12\sqrt{2})\\\\A=144\ ft

erik [133]3 years ago
6 0

ANSWER

Area = 144 {ft}^{2}

EXPLANATION

We use the sine ratio to find the missing side.

\sin(45 \degree)  =  \frac{AC}{24}

24\sin(45 \degree) = AC

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

AC = 12 \sqrt{2} ft

The triangle is a right isosceles triangle.

This implies that,

AC=BC=12√2 ft.

The area of the triangle is:

Area =  \frac{1}{2} bh

We substitute the values to get,

Area =  \frac{1}{2}  \times 12 \sqrt{2}  \times 12 \sqrt{2}

Area = 144 {ft}^{2}

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