Problem
Each side runs from a center to a point on that circle (a lens tip), so each side equals the radius.
The distance from a center to any point on its circle is always the radius.
3.G.A.1Draw A DiagramThe rhombus has 4 equal sides and perimeter 28 cm, so divide to find one side, which is the radius: 28 ÷ 4 = 7 cm.
Perimeter of a polygon is the sum of its sides; equal sides let us divide, a Grade 3 perimeter idea.
3.MD.D.8Identify SubproblemsAB joins the two centers; since each circle passes through the other's center, that distance is one radius: AB = 7 cm.
If a point sits on a circle, it is exactly one radius from that circle's center -- and the far center sits right on the circle.
3.G.A.1Draw A DiagramThe segment AB joining the two circle centers is exactly one radius long, the same length as each side of the shaded rhombus.
AB and every side of the rhombus are all radii of these equal circles, so they are lengths equal to the same radius and therefore equal to one another.
AB is a radius: it runs from circle A's center to center B, and center B lies right on circle A because each circle is drawn to pass through the other's center, so AB reaches from the center out to a point on the circle.
From a circle's center the straight distance out to any point on the circle is always the same length, the radius, since a circle is exactly the points sitting that one distance from the center.
Each rhombus side is a radius: every side runs from a circle's center to a lens tip, and each lens tip is a point sitting on that circle.
From a circle's center the straight distance out to any point on the circle is always the same length, the radius, since a circle is exactly the points sitting that one distance from the center.
Once AB equals one radius and each side equals that same radius, AB and a side are two lengths equal to the same thing, so they must be equal to each other.
Every side is a radius, so divide the perimeter by 4 -- and since each circle reaches the other's center, the segment between centers is that same radius!