Question

the sides KI and TE of a quadrilateral KITE are extended to the points A and B respectively . then /_ BTI + /_EKI equals
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Answer 1

Step-by-step explanation:

Correct answer:

40

Explanation:

The area of a kite is half the product of the diagonals.

A=p⋅q2

The diagonals of the kite are the height and width of the rectangle it is superimposed in, and we know that because the area of a rectangle is base times height.

Therefore our equation becomes:

A=l⋅w2.

We also know the area of the rectangle is A=l⋅w=80. Substituting this value in we get the following:

A=l⋅w2=802=40

Thus,, the area of the kite is 40.

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Find The Length Of The Diagonal Of A Kite : Example Question #2

Given: Quadrilateral KITE such that KI¯¯¯¯¯¯¯≅KE¯¯¯¯¯¯¯¯, TI¯¯¯¯¯¯≅TE¯¯¯¯¯¯¯, m∠K=60∘, ∠T is a right angle, and diagonal IE¯¯¯¯¯¯ has length 24.

Give the length of diagonal KT¯¯¯¯¯¯¯¯.

Possible Answers:

12+122–√

24

12+123–√

122–√+123–√

None of the other responses is correct.

Correct answer:

12+123–√

Explanation:

The Quadrilateral KITE is shown below with its diagonals IE¯¯¯¯¯¯ and KT¯¯¯¯¯¯¯¯.

. We call the point of intersection X:

Kite

The diagonals of a quadrilateral with two pairs of adjacent congruent sides - a kite - are perpendicular; also, KT¯¯¯¯¯¯¯¯ bisects the 60∘ and 90∘angles of the kite. Consequently, △KXI is a 30-60-90 triangle and △TXI is a 45-45-90 triangle. Also, the diagonal that connects the common vertices of the pairs of adjacent sides bisects the other diagonal, making X the midpoint of IE¯¯¯¯¯¯. Therefore,

IX=12⋅IE=12⋅24=12.

By the 30-60-90 Theorem, since IX¯¯¯¯¯¯¯ and KX¯¯¯¯¯¯¯¯¯ are the short and long legs of △KXI,

KX=IX⋅3–√=123–√

By the 45-45-90 Theorem, since IX¯¯¯¯¯¯¯ and XT¯¯¯¯¯¯¯¯ are the legs of a 45-45-90 Theorem,

XT=IX=12.

The diagonal KT¯¯¯¯¯¯¯¯ has length

KT=XT+KX=12+123–√.

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Find The Length Of The Diagonal Of A Kite : Example Question #3