


measurements:   a = 12 cm  b = 50 cm c = a   h = 70 cm   x = 56 cm

The object are  symmetrical

The perimeter of the blue object is: Answer cm

The perimeter of one of the grey triangles is : Answer cm

The area of one of the grey triangles is: Answer cm2

Find the area of the blue shape: Answer cm2

To solve this problem, let's first break it down based on the information provided and the symmetry of the object. 

Given:
- \( a = 12 \) cm
- \( b = 50 \) cm
- \( c = a = 12 \) cm
- \( h = 70 \) cm
- \( x = 56 \) cm

We have a symmetrical object, which consists of grey triangles and a blue shape. I'll start by calculating the required values step by step.

### 1. **Perimeter of the Blue Object**
To find the perimeter of the blue object, we need to know the shape and its sides. Since the shape is symmetrical and you provided \( a = 12 \) cm, \( b = 50 \) cm, and \( c = 12 \) cm, I'll assume it's a shape where these lengths are the sides.

Assuming the blue shape has two sides of \( a = 12 \) cm and \( b = 50 \) cm, the perimeter would be:
\[
\text{Perimeter of blue object} = a + b + c + b = 12 + 50 + 12 + 50 = 124 \text{ cm}
\]

### 2. **Perimeter of One of the Grey Triangles**
The grey triangles share one side with the blue object. If the grey triangle has sides \( a \), \( h \), and \( c \), the perimeter is:
\[
\text{Perimeter of one grey triangle} = a + h + c = 12 + 70 + 12 = 94 \text{ cm}
\]

### 3. **Area of One of the Grey Triangles**
The area \( A \) of a triangle is calculated as:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the grey triangle, with base \( a = 12 \) cm and height \( h = 70 \) cm:
\[
A = \frac{1}{2} \times 12 \times 70 = 6 \times 70 = 420 \text{ cm}^2
\]

### 4. **Area of the Blue Shape**
The area of the blue shape requires knowing the exact shape. However, assuming it’s a rectangle or another simple polygon involving the dimensions provided, and knowing it shares sides with the grey triangles, the area might be computed differently. But if we assume a simplified case, such as a rectangle:
\[
\text{Area of the blue shape} = b \times x = 50 \times 56 = 2800 \text{ cm}^2
\]

### Final Answers:
1. **Perimeter of the blue object**: 124 cm
2. **Perimeter of one of the grey triangles**: 94 cm
3. **Area of one of the grey triangles**: 420 cm\(^2\)
4. **Area of the blue shape**: 2800 cm\(^2\)

Would you like further details or have any questions about these calculations?

### Related Questions:
1. How would the calculations change if the dimensions were doubled?
2. What would be the perimeter if the blue shape were a triangle?
3. Can you find the area if the blue shape had a different length for \( x \)?
4. What happens to the perimeter of the grey triangle if the height \( h \) is reduced by half?
5. How can you verify the area of the blue shape using another method?

### Tip:
Always ensure that you understand the shape and its symmetry before beginning perimeter or area calculations to avoid errors in complex geometries.

Learn how to calculate the perimeter and area of symmetrical objects using given dimensions. This problem involves finding the perimeter of a blue shape and grey triangles, as well as the area of these triangles and the blue shape. Suitable for high school students.

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