Question

Sketch the following to help answer the question. Kite WXYZ has a short diagonal of XZ and a long diagonal of WY. The diagonals intersect at point V. The length of XZ = 8cm, the length of segment WV is 6√3, and the ∠XYV = 30°. Find the exact area of kite WXYZ.

Answer 1

Answer: 69.281cm2

Step-by-step explanation: first we sketch the kite, which I have done is the picture attached

To find the area, we divide the kite into two triangles, cutting the kite at the line XZ

So we have two triangles, XWZ and XYZ

We know that finding the area of a triangle is half of it's base multiplied by the height

A = 1/2bh

For triangle XWZ we have a base of 8cm and a height of 6root3cm

Finding the area

1/2 x 8 x 6root3 = 41.569cm2

For triangle XYZ we have the base, but we don't have the height

So to get the height we use tan rule

We states that tan of an acute angle in a right angle triangle equals to the value of the length opposite the angle divided by the value of the length adjacent to it, popular known as "TOA"

Since XY and XZ are the same lengths (properties of a kite)

We can tell that XV is half of XZ

So XV = 8/2 = 4cm

We label the height we are looking for as x

So therefore

Tan30 = 4/x

xtan30 = 4

x = 4/tan30 = 6.928

So therefore

Area of triangle XYZ

1/2 x 8 x 6.928 = 27.712cm2

Adding the two Areas together = 41.569+27.712 = 69.28cm2

Answer 2

The answer is: 40 sqr3

I know that this is correct is OW :) Ya'll have a nice day! Good luck!