A composite figure is made up of an isosceles triangle with two equal sides of 7 cm ech and a base of 5 cm and a width of 3cm. If the base of the triangle is share with one side of the rectangle, what is the perimeter of the composite figure?

The composite figure is made up of an isosceles triangle and a rectangle, where the base of the triangle is shared with one side of the rectangle. Let's break it down step by step:

### Given:
- The isosceles triangle has two equal sides of 7 cm each and a base of 5 cm.
- The rectangle shares its base with the triangle, so one side of the rectangle is 5 cm (the same as the base of the triangle).
- The width (height) of the rectangle is 3 cm.

### Step 1: Perimeter of the Triangle
The perimeter \( P_{triangle} \) of the isosceles triangle is the sum of its three sides:
\[
P_{triangle} = 7 \, \text{cm} + 7 \, \text{cm} + 5 \, \text{cm} = 19 \, \text{cm}.
\]

### Step 2: Perimeter of the Rectangle
The perimeter \( P_{rectangle} \) of a rectangle is given by:
\[
P_{rectangle} = 2 \times (\text{length} + \text{width}).
\]
Here, the length is the base of the triangle (5 cm), and the width is given as 3 cm. Therefore:
\[
P_{rectangle} = 2 \times (5 \, \text{cm} + 3 \, \text{cm}) = 2 \times 8 \, \text{cm} = 16 \, \text{cm}.
\]

### Step 3: Perimeter of the Composite Figure
For the composite figure, the base of the triangle and the top side of the rectangle (both measuring 5 cm) are shared. Since this side is counted twice in the total perimeter of both shapes, we subtract it once:
\[
P_{composite} = P_{triangle} + P_{rectangle} - 5 \, \text{cm}.
\]
Substituting the values:
\[
P_{composite} = 19 \, \text{cm} + 16 \, \text{cm} - 5 \, \text{cm} = 30 \, \text{cm}.
\]

### Final Answer:
The perimeter of the composite figure is **30 cm**.

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. What would the perimeter be if the rectangle’s width was 5 cm instead of 3 cm?
2. How does the perimeter change if the triangle’s base increases by 2 cm?
3. What is the area of the composite figure?
4. How do you calculate the perimeter of a composite figure with a different shape attached?
5. How does the shape of the triangle affect the overall perimeter of the composite figure?

**Tip:** When working with composite figures, always subtract any shared sides that are counted twice when calculating the perimeter.

A composite figure is made up of an isosceles triangle with two equal sides of 7 cm each and a base of 5 cm and a width of 3 cm. If the base of the triangle is shared with one side of the rectangle, what is the perimeter of the composite figure?

Learn how to find the perimeter of a composite figure consisting of an isosceles triangle and a rectangle. The triangle has two sides of 7 cm each, a base of 5 cm, and the rectangle has a width of 3 cm. This solution breaks down the steps and key formulas for calculating the perimeter, suitable for students in Grades 6-8.

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