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:

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

### Sample Test Question

1. 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?
2. 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?