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Using the dimensions provided in the attached shape, calculate the perimeter, Estimated  and area. Check your answer for reasonableness using estimation. 

To calculate the perimeter and area of this shape, I'll break down the analysis:

### Step 1: Analyze the Shape
The given diagram shows a combination of a rectangle and a right-angled triangle on top of it. The dimensions provided are:
- Height of the entire figure: 17.8 cm.
- Width of the rectangle: 12.5 cm.

### Step 2: Break Down the Shape
1. **Rectangle**:
   - Height = \( h_1 \) (unknown, the height of the rectangle).
   - Width = 12.5 cm.

2. **Right-Angled Triangle** (on top of the rectangle):
   - Base = 12.5 cm (same as the width of the rectangle).
   - Total height = 17.8 cm, so the height of the triangle = \( 17.8 \, \text{cm} - h_1 \).

### Step 3: Calculate the Perimeter
To calculate the perimeter, we need all sides:
1. The perimeter of the rectangle part = \( 2 \times (h_1 + 12.5 \, \text{cm}) \).
2. The hypotenuse of the triangle can be found using the Pythagorean theorem:
   \[
   \text{Hypotenuse} = \sqrt{(12.5)^2 + (17.8 - h_1)^2}
   \]
3. Add up the sides to get the total perimeter.

### Step 4: Calculate the Area
The total area is the sum of the areas of the rectangle and the triangle:
1. **Area of the Rectangle**:
   \[
   \text{Area of Rectangle} = 12.5 \times h_1
   \]
2. **Area of the Triangle**:
   \[
   \text{Area of Triangle} = \frac{1}{2} \times 12.5 \times (17.8 - h_1)
   \]
3. **Total Area**:
   \[
   \text{Total Area} = (12.5 \times h_1) + \frac{1}{2} \times 12.5 \times (17.8 - h_1)
   \]

### Step 5: Estimation for Reasonableness
1. Consider the whole shape roughly as a rectangle with the dimensions 12.5 cm × 17.8 cm.
2. Approximate perimeter and area using those dimensions to ensure the calculated values make sense.

Would you like me to continue with the detailed calculations and determine \( h_1 \)?

Using the dimensions provided in the attached shape, calculate the perimeter and area. Check your answer for reasonableness using estimation.

Calculate the perimeter and area of a shape that combines a rectangle and a right-angled triangle. Dimensions are 17.8 cm in height and 12.5 cm in width. Learn how to apply the Pythagorean Theorem and area formulas to solve this problem. Suitable for students in Grades 7-9.

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