Question

HELP PLEASE
What is the area of the kite below?

Answer 1

Answer: A = 33 in²

Explanation:

Given information:

Longer side = 7 in

Shorter side = 4 in

Shorter Hypotenuse = 5 in

Given formula:

A = (1/2) × (d₁) × (d₂)

• A = area
• d₁ = The longer line (horizontal)
• d₂ = The shorter line (vertical)

Please refer to the attachment below for a graphical understanding

Determine the length of the shorter side (vertical) through the Pythagorean theorem

a² + b² = c² (Pythagorean theorem)

(4)² + b² = (5)² (Substitute values into the equation)

16 + b² = 25

b² = 25 - 16

b² = 9

b = 3 or b = -3 (rej)

Substitute values into the given formula

A = (1/2) × d₁ × d₂

A = (1/2) × (7 + 4) × (3 + 3)

Simplify values in the parenthesis

A = (1/2) × 11 × 6

Simplify by multiplication

A = (11/2) × 6

`\Large\boxed{A=33}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

Area = 33 inches squared

Explanation:

The formula for the area of a kite is:

Area = ½ × (d)1 × (d)2

To find the first diagonal (d1):

d1 = 7 in + 4 in = 11 in

To find the second diagonal (d2):

The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.

d2 = 3 in + 3 in = 6 in

Now we can plug the diagonals into the area formula.

Area = ½ × 11 × 6 = 33 inches squared