Question

Complete the steps to find the area of the kite. What is GE? Square root of units What is DF? Square root of units What is the area of the kite to the nearest unit? square unit?

Answer 1

320
80
80
Thats what it is on edg

Answer 2

`GE=√(320)=8√(5)`

`DF=√(80)=4√(5)`

`\text{Area of kite}=80`

Explanation:

We have been given an image of a kite on coordinate plane.

To find the length of GE we will use distance formula:

`\text{Distance}=√((x_2-x_1)^2+(y_2-y_1)^2)`

Upon substituting coordinates of point G and E in above formula we will get,

`GE=√((16-0)^2+(8-0)^2)`

`GE=√((16)^2+(8)^2)`

`GE=√(256+64)`

`GE=√(320)`

`GE=8√(5)`

Therefore, the length of diagonal GE is
`8√(5)` units.

Similarly we will find the length of diagonal DF using distance formula.

`DF=√((14-10)^2+(2-10)^2)`

`DF=√((4)^2+(-8)^2)`

`DF=√(16+64)`

`DF=√(80)`

`DF=4√(5)`

Therefore, the length of diagonal DF is
`4√(5)` units.

Now we will use area of kite formula to find the area of our given kite.

`\text{Area of kite}=(p*q)/(2)`, where, p and q are diagonals of kite.

Upon substituting our values in area formula we will get,

`\text{Area of kite}=(8√(5)*4√(5))/(2)`

`\text{Area of kite}=(32*5)/(2)`

`\text{Area of kite}=16*5`

`\text{Area of kite}=80`

Therefore, area of our given kite is 80 square units.