Chapter 8.2, Problem 30E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

# In Exercises 27 to 30, find the area of the figure shown. Given: Pentagon R S T V W with m ∠ V R S = m ∠ V S R = 60 ° ,   R S = 8 2 , and R W - ≅ W V - ≅ V T - ≅ T S - Find: A R S T V W

To determine

To Find:

Area of the pentagon provided.

Explanation

Formula Used:

1. Split the pentagon into three triangles and find the corresponding areas and then sum it up.

2. Pythagorean theorem for the right angle triangle âˆ†ABC for the hypotenuse AC,

AC2=AB2+BC2.

3. Sum of the angles in a triangle is 180Â°.

4. Area of right triangle =12bh, where b is the base and h is the height of the triangle.

5. Area of the equilateral triangle âˆ†ABC with each side of length s is given by AABC=Â S243.

Let the vertices of the provided pentagon be R,S,T,V and W.

Letâ€™s divide the pentagon into three triangles. That is, âˆ†RVW,Â Â âˆ†SVT and âˆ†RVS.

It is given that âˆ VSR=mâˆ VSR=60Â°,Â RS=82, and RW-â‰…WV-â‰…VT-â‰…TS-.

Now consider the triangle âˆ†RVS,

Here mâˆ VRS=mâˆ VSR=60Â° and RS=82.

mâˆ VRS+mâˆ VSR+Â mâˆ RVS=180Â°

mâˆ RVS=180Â°-120Â°=60Â°

Therefore, âˆ†RVS is an equilateral triangle.

Area of the equilateral triangle =Â S243, s is the side lengths

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