Question

mr. johnson has a garden in the shape of a kite with a length of 5 feet and a width of 4 feet. a bag of topsoil covers 10 square feet. the area of each triangle is ft². the area of the garden is ft². the number of bags of topsoil needed is

Explanation:

Step1: Calculate the area of each triangle

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, assume the base \(b = 5\) feet and height \(h=2\) feet (since the width of the kite is \(4\) feet and the kite is made of two congruent triangles with respect to one of its diagonals).
\(A=\frac{1}{2}\times5\times2 = 5\) square feet.

Step2: Calculate the area of the garden (kite)

The garden (kite) is composed of \(2\) congruent triangles. So the area of the kite \(A_{kite}=2\times A_{triangle}\).
Since \(A_{triangle} = 5\) square feet, \(A_{kite}=2\times5=10\) square feet.

Step3: Calculate the number of top - soil bags

If one bag of top - soil covers \(10\) square feet and the area of the garden is \(10\) square feet. Using the formula \(n=\frac{A_{kite}}{A_{per\ bag}}\), where \(A_{kite}\) is the area of the garden and \(A_{per\ bag}\) is the area covered by one bag.
\(n=\frac{10}{10}=1\)

Answer:

The area of each triangle is \(5\) \(ft^{2}\).
The area of the garden is \(10\) \(ft^{2}\).
The number of bags of topsoil needed is \(1\).