Francisco is building a window seat below a bay window in the shape of an isosceles trapezoid. His blueprint for the window seat is shown.%0D%0A%0D%0A%0D%0A%0D%0A*Picture not drawn to scale%0D%0A%0D%0AWhat is the area of the window seat?
To find the area of the window seat, we need to calculate the area of the isosceles trapezoid.
The formula for the area of a trapezoid is given by:
Area = (1/2) * (a + b) * h
Where:
a = length of the top base of the trapezoid = 5 feet
b = length of the bottom base of the trapezoid = 8 feet
h = height of the trapezoid = 3 feet
Plugging in the values:
Area = (1/2) * (5 + 8) * 3
Area = (1/2) * 13 * 3
Area = 6.5 * 3
Area = 19.5 square feet
Therefore, the area of the window seat is 19.5 square feet.
that isnt the right answer
Apologies for the mistake. Let's correct it.
To find the area of the isosceles trapezoid, we need to break it down into two parts: a rectangle and a right triangle.
1. The rectangle:
The width of the rectangle is the same as the top base of the trapezoid = 5 feet.
The length of the rectangle is the same as the height of the trapezoid = 3 feet.
Area of the rectangle = width * length = 5 feet * 3 feet = 15 square feet.
2. The right triangle:
The base of the right triangle is the difference between the bottom base and the top base of the trapezoid = 8 feet - 5 feet = 3 feet.
The height of the right triangle is the same as the height of the trapezoid = 3 feet.
Area of the right triangle = (1/2) * base * height = (1/2) * 3 feet * 3 feet = 4.5 square feet.
Now, to find the total area of the window seat, we add the area of the rectangle and the right triangle:
Total area = Area of rectangle + Area of right triangle
Total area = 15 square feet + 4.5 square feet
Total area = 19.5 square feet
Therefore, the correct area of the window seat is 19.5 square feet.