   Chapter 11.4, Problem 16E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

In Exercises 15 and 16, find the area of the given figure. Give the answer to the nearest tenth of a square unit. Trapezoid

To determine

To find:

The area of the given figure

Explanation

Approach:

Finding the area of the figure is followed by identifying the figure and find area with the suitable geometry formulae.

Calculation:

Given,

The area of the given figure (A)= The area of the triangle (MRQ)(A1)+ The area of the square RSPQ(A2)+ The area of the triangle SNP(A3)

The area of the triangle (MRQ)(A1):

For ΔRMQ

α+β+γ=180

Here α=70 and γ=90

70+β+90=180

160+β=180

Add 160 on both sides,

160+β160=180160

β=20

Here,

β=20

a=5 in.,

c=6 in.

Area of the triangle (A1)=12acsinβ

12(5)(6)sin20

=(5)(3)sin20

=(15)sin20

=(15)(0.34)

A1=5.1 in2.

The area of the square (RSPQ)(A2):

Side (s)=6 in.

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