To find the perimeter of a joint figure first find out what simpler figures the whole figures is made of. For example, two right-angled triangles and a rectangle all of equal height can be joined together to make a trapezium, or trapezoid. You then need to identify the common edges, because these will not form part of the perimeter, and you need to identify the exposed edges, because these will form part of the perimeter. So going back to the trapezium, the heights of the triangles and two sides of the rectangle are common, so these will be excluded, but the hypotenuses of the triangles and the other two sides are exposed, so they form part of the perimeter.
You need to know the lengths of the exposed edges. Although the common height is not part of the perimeter, you may need it to work out the lengths of the exposed sides or edges. For the triangles you need the lengths of the hypotenuses, so, using whatever information you have about the triangles, find the lengths of the hypotenuses. You may need Pythogars' theorem or trigonometry to do this, depending on whether you are given the lengths of sides or angle measurements. The rectangle length or width will be exposed, and so you need to work out their length from the info you have. The perimeter will be the sum of the two hypotenuses and bases of the triangles, plus twice the length (or width) of the rectangle.
Another example is a triangle attached to a semicircle, so that one side of the triangle is a diameter of the semicircle. The length of the circumference of a circle is 2(pi)r, where r is the radius, so (pi)r is the exposed part of the semicircle. You need the lengths of the exposed sides of the triangle. 2r is the length of one side, and you need more info about the triangle to work out the length of the other two sides. Combine these to get the perimeter of the whole figure.
These are just examples. You need to examine closely how your joint figure has been made. You might like to work out the perimeter of a regular 5-pointed star built on a regular pentagon. Here you have a pentagon with five isosceles triangles sitting on its sides, but none of the sides of the pentagon are exposed and two sides of each triangle, all with the same length are exposed, so the perimeter is ten times the length of just one side of a triangle. You need info about the pentagon to work out the length of this side.
