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.
i need help fast!
17 * 22 = ? cm^2
To calculate the area of the composite figure, we need to first determine the individual areas of the rectangle and the right triangle.
1. Area of the rectangle:
The top and bottom horizontal edges of the rectangle measure 17 centimeters, and the left vertical edge measures 22 centimeters. Since the opposite sides of a rectangle are equal in length, we can consider the top and bottom edges as the base, and the left vertical edge as the height.
Area of the rectangle = base × height
= 17 cm × 22 cm
= 374 cm²
2. Area of the right triangle:
The right triangle is formed by the left vertical edge of the rectangle (which measures 22 centimeters) as the hypotenuse and the bottom horizontal edge of the rectangle (which measures 17 centimeters) as one of the legs. To find the area of the right triangle, we need to determine the length of the other leg.
Using the Pythagorean theorem, we can calculate the length of the other leg:
leg² + leg² = hypotenuse²
leg² + 17² = 22²
leg² + 289 = 484
leg² = 484 - 289
leg² = 195
leg ≈ √195
leg ≈ 13.96 cm (rounded to two decimal places)
Area of the right triangle = (base × height) / 2
= (17 cm × 13.96 cm) / 2
≈ 118.86 cm²
3. Total area of the composite figure:
Since the composite figure consists of a rectangle and a right triangle, we can calculate the total area by summing up the individual areas.
Total area = Area of rectangle + Area of right triangle
= 374 cm² + 118.86 cm²
= 492.86 cm²
Therefore, the area of the composite figure is approximately 492.86 cm².