The perimeter of a compound shape is the total length of the outer boundaries of the shape. In a compound shape, the perimeter is the sum of the lengths of all the sides of the individual shapes that make up the compound shape. If there are missing lengths in a compound shape, you can use known lengths and basic math principles to solve for the missing lengths and find the perimeter of the compound shape.

To find the perimeter of a compound shape with missing lengths, you can follow these steps:

- Identify the lengths that you already know.
- Add up all of the known lengths to find the total perimeter of the shape.
- If there is a missing length, use the given perimeter to set up an equation to solve for the missing length.
- Solve the equation to find the missing length.
- Add the missing length to the total perimeter to find the final perimeter of the compound shape.

### Sample Test Question

- A compound shape is made up of a rectangle and a triangle, as shown below: [asy] unitsize(1cm); defaultpen(linewidth(0.8pt)); pair A=(0,0), B=(5,0), C=(5,5), D=(0,5), E=(5,5), F=(5,7), G=(0,7); draw(A–B–C–D–cycle); draw(E–F–G–cycle); label(“$x$”,(A+D)/2,W); label(“$y$”,(E+F)/2,N); label(“$5$”,(B+C)/2,S); label(“$3$”,(F+G)/2,N); [/asy] The perimeter of this compound shape is 16. What is the value of x?
- A compound shape is made up of a square and a triangle, as shown below: [asy] unitsize(1cm); defaultpen(linewidth(0.8pt)); pair A=(0,0), B=(5,0), C=(5,5), D=(0,5), E=(5,5), F=(5,7), G=(0,7); draw(A–B–C–D–cycle); draw(E–F–G–cycle); label(“$x$”,(A+D)/2,W); label(“$y$”,(E+F)/2,N); label(“$5$”,(B+C)/2,S); label(“$3$”,(F+G)/2,N); [/asy] The perimeter of this compound shape is 18. What is the value of y?

#### Answer

To solve the first question, we can set up the following equation: 5 + 5 + 3 + y = 16. We know that y = 5, so we can substitute this value into the equation to find x: 5 + 5 + 3 + 5 = 16. Solving this equation, we find that x = 3. Therefore, the value of x is 3.

To solve the second question, we can set up the following equation: 5 + 5 + x + 3 = 18. We know that x = 5, so we can substitute this value into the equation to find y: 5 + 5 + 5 + 3 = 18. Solving this equation, we find that y = 5. Therefore, the value of y is 5.

## Perimeter Of Compound Shapes With Missing Lengths Worksheet

**Download PDF: Perimeter Of Compound Shapes With Missing Lengths**