a garden in the shape of a square measures 15 feet on each side. A triangular paved patio is in the center. It has a base of 10 feet and a height of 8 feet. What is the area of the garden?

The area occupied by the garden is 185 square feet.

Step-by-step explanation:

Step 1; To find the area occupied by the garden we have to subtract the area that the patio covers from the area of the garden without the patio. We need to determine the area of the garden without including the patio and the area of the patio. Then subtract them from each other in order to determine the area of the garden.

Step 2; It is given that the garden is a square. The area occupied the garden can thus be found by substituting the area occupied by a square. A side on the square measures 15 feet and the area covered by any square is given by squaring its side's length.

Area of Garden without patio = 15 * 15 = 225 square feet.

Now we have to find the area of the patio. The patio is in the shape of a triangle which has a height of 8 feet and a base length of 10 feet. The area occupied by a triangle is 0.5 times the multiplication of its base length and height.

Area of triangular patio = 0.5 * 8 * 10 = 0.5 * 80 = 40 square feet.

Step 3; Now to find the actual area of the garden we minus the area occupied by the patio from the area of the garden without the patio.

Actual Area of garden = area of garden without patio - area of patio = 225 square feet - 40 square feet = 185 square feet.