Find area and perimeter of the shaded region.
Show work
7cm
5cm
5cm
5cm
5cm
7cm
18cm
Unfortunately, we cannot determine which region is shaded without a diagram or image. Could you please provide more information?
To find the area and perimeter of the shaded region, we need to break it down into different shapes.
First, let's calculate the area of the shaded region:
1. The shaded area consists of three rectangles. Let's find their individual areas:
- First rectangle: 7 cm (length) × 5 cm (width) = 35 cm²
- Second rectangle: 5 cm (length) × 5 cm (width) = 25 cm²
- Third rectangle: 7 cm (length) × 5 cm (width) = 35 cm²
2. The shaded area also contains two triangles. Let's calculate their individual areas:
- First triangle: (1/2) × 7 cm (base) × 18 cm (height) = 63 cm²
- Second triangle: (1/2) × 5 cm (base) × 18 cm (height) = 45 cm²
3. To find the total area of the shaded region, add the areas of all the shapes:
Total area = 35 cm² + 25 cm² + 35 cm² + 63 cm² + 45 cm²
= 203 cm²
Therefore, the area of the shaded region is 203 cm².
Now, let's calculate the perimeter of the shaded region:
1. The shaded area consists of three rectangles. Let's find their individual perimeters:
- First rectangle: 2 × (7 cm + 5 cm) = 2 × 12 cm = 24 cm
- Second rectangle: 2 × (5 cm + 5 cm) = 2 × 10 cm = 20 cm
- Third rectangle: 2 × (7 cm + 5 cm) = 2 × 12 cm = 24 cm
2. The shaded area also contains two triangles. Let's calculate their individual perimeters:
- First triangle: The perimeter is the sum of all its sides. From the given dimensions, we have two sides measuring 7 cm and one side measuring 18 cm (hypotenuse). Perimeter = 7 cm + 7 cm + 18 cm = 32 cm
- Second triangle: The perimeter is the sum of all its sides. From the given dimensions, we have two sides measuring 5 cm and one side measuring 18 cm (hypotenuse). Perimeter = 5 cm + 5 cm + 18 cm = 28 cm
3. To find the total perimeter, add the perimeters of all the shapes:
Total perimeter = 24 cm + 20 cm + 24 cm + 32 cm + 28 cm
= 128 cm
Therefore, the perimeter of the shaded region is 128 cm.