Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The top horizontal edge of the rectangle measures 17 centimeters, the left vertical edge of the rectangle measures 22 centimeters, and the bottom horizontal edge measures 17 centimeters. The left vertical leg is on the right edge of the rectangle, with v
Calculate the area of the composite figure, which is not drawn to scale.
area of rectangle = length * width
area of triangle = 1/2 * length * width
surely the figure is composed of rectangles and triangles ...
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
The top horizontal edge of the rectangle measures 17 centimeters, the left vertical edge of the rectangle measures 22 centimeters, and the bottom horizontal edge measures 17 centimeters. The left vertical leg is on the right edge of the rectangle, with v
Calculate the area of the composite figure, which is not drawn to scale.
To calculate the area of the composite figure, we need to break it down into its constituent parts, which are a rectangle and a triangle.
Area of rectangle: length x width = 17 cm x 22 cm = 374 sq. cm
To calculate the area of the triangle, we first need to find the height, which is the vertical distance between the bottom horizontal edge and the slanted edge of the triangle. We can use Pythagoras' theorem to find the height:
h^2 = v^2 + w^2
where h is the height, v is the length of the vertical leg of the triangle, and w is the width of the rectangle.
Since the vertical leg of the triangle is the same length as the width of the rectangle, we have:
h^2 = v^2 + 17^2
Since the hypotenuse of the triangle is also the diagonal of the rectangle, we have:
v^2 + w^2 = d^2
where d is the length of the diagonal, which we can calculate using Pythagoras' theorem:
d^2 = 17^2 + 22^2
Combining these equations, we get:
h^2 = (d^2 - 17^2) + 17^2
h^2 = d^2 - 17^2
h = sqrt(d^2 - 17^2) = sqrt(22^2 + 17^2 - 17^2) = sqrt(22^2) = 22 cm
Now we can calculate the area of the triangle:
Area of triangle: 1/2 x base x height = 1/2 x 17 cm x 22 cm = 187 sq. cm
Therefore, the total area of the composite figure is:
Total area = area of rectangle + area of triangle = 374 sq. cm + 187 sq. cm = 561 sq. cm
To find the area of the composite figure, we need to calculate the area of the rectangle and subtract the area of the triangle.
1. Calculate the area of the rectangle:
Since the top and bottom edges of the rectangle have the same length (17 cm), we can multiply this by the height of the rectangle. The left vertical edge (22 cm) serves as the height of the rectangle.
Area of the rectangle = length × height
Area of the rectangle = 17 cm × 22 cm
2. Calculate the area of the triangle:
The triangle is formed by the right edge of the rectangle and the bottom horizontal edge. To find the area of this triangle, we can use the formula:
Area of a triangle = ½ × base × height
The base is the length of the bottom horizontal edge (17 cm), and the height is the length of the right vertical edge (v) minus the length of the bottom horizontal edge (17 cm).
Area of the triangle = ½ × 17 cm × (v - 17 cm)
3. Calculate the area of the composite figure:
To find the area of the composite figure, we subtract the area of the triangle from the area of the rectangle:
Area of the composite figure = Area of the rectangle - Area of the triangle
So, the area of the composite figure is given by:
Area of the composite figure = (17 cm × 22 cm) - ½ × 17 cm × (v - 17 cm)
Note: You would need to know the value of "v" to calculate the exact area of the composite figure.