   Chapter 8.2, Problem 30E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# 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 ABC for the hypotenuse AC,

AC2=AB2+BC2.

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

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 ABC with each side of length s is given by AABC= S243.

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

Let’s divide the pentagon into three triangles. That is, RVW,  SVT and RVS.

It is given that VSR=mVSR=60°, RS=82, and RW-WV-VT-TS-.

Now consider the triangle RVS,

Here mVRS=mVSR=60° and RS=82.

mVRS+mVSR+ mRVS=180°

mRVS=180°-120°=60°

Therefore, RVS is an equilateral triangle.

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

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