Video: Finding the Diagonal Length of a Kite given Its Area and the Other Diagonal Length

𝐴𝐡𝐢𝐷 is a kite where 𝐴𝐢 = 23 in and its area equals 115 in². Determine the length of 𝐡𝐷.


Video Transcript

𝐴𝐡𝐢𝐷 is a kite where 𝐴𝐢 is equal to 23 inches and its area equals 115 square inches. Determine the length of 𝐡𝐷.

So we’ve been told the area of a kite and the length of one of its diagonals 𝐴𝐢. Our task is to calculate the length of the second diagonal. In order to do so, we need to recall the formula for calculating the area of a kite.

If a kite has diagonals 𝑑 one and 𝑑 two, then its area can be found by calculating half of their product. In this question, the two diagonals of the kite are the lines 𝐴𝐢 and 𝐡𝐷. And therefore, we have that the area is equal to one-half of the length of 𝐴𝐢 multiplied by the length of 𝐡𝐷.

Remember, we’ve been given the area and the length of 𝐴𝐢. Let’s substitute these values into the formula. We now have that 115 is equal to a half multiplied by 23 multiplied by 𝐡𝐷. In order to find the length of 𝐡𝐷, we need to solve this equation.

The first step is to eliminate the fraction on the right-hand side by multiplying both sides of the equation by two. This gives 230 is equal to 23 multiplied by 𝐡𝐷.

The final step to solve for 𝐡𝐷 is to divide both sides of the equation by 23. 230 divided by 23 is 10. And so we have that 10 is equal to 𝐡𝐷. Therefore, the length of 𝐡𝐷, which is the second diagonal of this kite, is 10 inches.

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