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.