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.
3 answers
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.
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
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
52 answers