Given
A
C
=
30
centimeters and
B
E
=
7
centimeters, determine the area of the kite.
The figure shows a kite with vertices labeled as Upper A, Upper B, Upper C, and Upper D. Dotted lines are drawn from Upper A to Upper C and from Upper B to Upper D, which intersect at a point labeled as Upper E. The length of the sides UpperWord AB and UpperWord AD is labeled as 10 centimeters, and the length of the sides UpperWord BC and UpperWord DC is labeled as 23 centimeters.
The area of the kite ABCD is
square centimeters.
Well, well, well, we have a kite here! And what a fancy one it is. So, to find the area of this kite, we can use the good old formula: area equals half the product of the diagonals.
In this case, the diagonals AC and BE are given as 30 cm and 7 cm, respectively. So, the area of the kite is:
Area = 1/2 * AC * BE
Area = 1/2 * 30 cm * 7 cm
Area = 105 square cm
Voila! The area of this fancy kite is 105 square centimeters.
To find the area of a kite, we can use the formula:
Area = 1/2 * diagonal1 * diagonal2
In this case, the diagonals are AC and BE.
Given:
AC = 30 centimeters
BE = 7 centimeters
Now, let's find the lengths of the diagonals.
For diagonal AC:
We have two adjacent sides of the kite AB and BC, and we can find the value of missing side AC using the Pythagorean theorem:
AC^2 = AB^2 + BC^2
AC^2 = 10^2 + 23^2
AC^2 = 100 + 529
AC^2 = 629
AC ≈ √629
Now, let's calculate the length of diagonal AC:
AC ≈ √629 ≈ 25.079 centimeters
For diagonal BE:
Given, BE = 7 centimeters
Now that we have the lengths of both diagonals AC and BE, we can calculate the area of the kite using the formula:
Area = 1/2 * AC * BE
Plugging in the values:
Area = 1/2 * 25.079 * 7
Area ≈ 87.7665 square centimeters
Therefore, the area of the kite ABCD is approximately 87.7665 square centimeters.
You could have just said:
The figure shows a kite with vertices labeled A, B, C, and D. Dotted lines are drawn from A to C and from B to D, which intersect at a point labeled as E. The length of the sides AB and AD is labeled as 10 centimeters, and the length of the sides BC and DC is labeled as 23 centimeters.
Look at triangle ABC, you know all the sides, so we could find angle B by the cosine law:
30^2 = 10^2 + 23^2 - 2(10)(23)cos B
I found B ≐ 126.1°
So now the area of ∆ABC = (1/2)(10)(23)sin 126.1°, which would be half the area of the kite