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6

Solution by Steps

step 1

The number 6 can be represented in various forms

step 2

In decimal form, it is simply 6

step 3

In word form, it is "six"

step 4

In Roman numerals, it is "VI"

step 5

In the context of shapes, a regular hexagon has 6 sides

step 6

In binary form, it is "110_2"

Answer

6, six, VI, regular hexagon, 110_2

Key Concept

Representation of the number 6

Explanation

The number 6 can be represented in different forms such as decimal, word, Roman numeral, shape, and binary.

Solution by Steps

step 1

Given the area of rectangle

ABCD

is

666

square centimeters, and the lengths

BE = 11

cm and

DF = 6

cm

step 2

To find the area of triangle

AEF

, we need to determine the base and height of the triangle

step 3

Since

BE

is perpendicular to

AEG

,

BE

can be considered as the height of triangle

AEF

step 4

The length

DF

is not directly useful for finding the area of triangle

AEF

step 5

The base of triangle

AEF

is the length

AF

. Since

AF

is not given directly, we need to use the properties of the rectangle to find it

step 6

The length of

BC

is given as

666

cm. Since

BE = 11

cm, the remaining length

EC

is

666 - 11 = 655

cm

step 7

Since

E

lies on

BC

and

F

lies on

CD

, and

DF = 6

cm, the length

AF

can be considered as the diagonal of the rectangle minus the length

DF

step 8

The area of triangle

AEF

can be calculated using the formula for the area of a triangle:

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

step 9

Substituting the values, we get

\text{Area} = \frac{1}{2} \times 655 \times 11 = 3602.5

square centimeters

Answer

3602.5 square centimeters

Key Concept

Area of a triangle

Explanation

The area of a triangle is calculated using the formula

\frac{1}{2} \times \text{base} \times \text{height}

. In this problem, the base and height were determined using the given dimensions of the rectangle and the properties of the triangle within it.

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