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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Chapter
Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

For equilateral Δ ARST, RT = 6. Squares and triangles on the sides of Δ RST determine hexagon ABCDEF. Find the area of ABCDEF.

To determine

To find:

The area of the hexagon.

Explanation

Concept:

1) The area of the square is given by, A = s2 where s is side of the square.

2) The area of a triangle can be expressed using the lengths of two sides and the sine of the included angle, A=12×absinC

3) The area of the equilateral triangle is given by, A=34s2 where s is side of the equilateral triangle.

Calculation:

It is given that the side of the square is 6 units.

Use the formula of area of the square, A = s2

Substitute s = 6 in A = s2.

Asquare=(6)2=36units2

It is given that the side of the equilateral triangle is 6 units.

Use the formula of area of the equilateral triangle, A=34s2

Substitute s=6 in A=34s2.

ARST=34(6)2=34(36)=15.59units2

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