In the figure above, AB = AD, BC = CD, BE = 2, BC = 4, and AC = 10. What is the area of triangle ABD?

In The Figure Above, AB = AD, BC = CD, BE = 2, BC = 4, And AC = 10. What Is The Area Of Triangle ABD?

Answers

Answer 1

The properties of items in a question can be used to simplify the solution to the questions

The area of triangle ΔABD is 20 - 4·√3

The reason the above value for the area of ΔABD is correct is as follows:

The given parameters are;

AB = AD, BC = CD, BE = 2, BC = 4, AC = 10

Given that AB = AD, and BC = CD, we have that the figure ABCD is a kite

AC is perpendicular to BD by properties of the diagonals of a kite

ΔBCE is a right triangle

By Pythagoras' theorem, [tex]\overline{CE}[/tex]² = [tex]\overline{BC}[/tex]² - [tex]\overline{BE}[/tex]²

Which gives;

[tex]\overline{CE}[/tex]² = 4² - 2² = 12

[tex]\overline{CE}[/tex] = 2·√3

Given that AC is the perpendicular bisector of BD, by the properties of a kite, we have;

BD = BE + DE, where BE = DE definition of bisected line

BD = BE + BE = 2·BE

Area of a triangle = (1/2) × Base length × Height

AE = The altitude (height) of the ΔABD = AC - CE

∴ AE = 10 - 2·√3

BD = The base length of ΔABD = 2·BE (Length of BE = 2)

∴ BD = 2 × 2 = 4

The area of triangle ΔABD = (1/2) × BD × AE

∴ The area of triangle ΔABD = (1/2) × 4 × (10 - 2·√3) = 20 - 4·√3

The area of triangle ΔABD = 20 - 4·√3

Learn more about the properties of a kite here:

https://brainly.com/question/24110637


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Step-by-step explanation:

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