10.6. Area and Perimeter of Rhombuses and Kites http://www.ck12.org
10.6 Area and Perimeter of Rhombuses and Kites
Here you’ll learn how to calculate the area and perimeter of rhombuses and kites.
What if you wanted to find the areas of different shapes on the Brazilian flag, pictured below? The flag has
dimensions of 20×14 (units vary depending on the size, so we will not use any here). The vertices of the yellow
rhombus in the middle are 1.7 units from the midpoint of each side.
Find the total area of the flag and the area of the rhombus (including the circle).Do not round your answers.After
completing this Concept, you’ll be able to answer this question using your knowledge of rhombuses.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52496CK-12 Foundation: Chapter10AreaandPerimeterofRhombusesandKitesA
Learn more about the area of kites and rhombuses by watching the video at this link.
Guidance
Recall that a rhombus is an equilateral quadrilateral and a kite has adjacent congruent sides. Both of these quadrilat-
erals have perpendicular diagonals, which is how we are going to find their areas.
Notice that the diagonals divide each quadrilateral into 4 triangles. In the rhombus, all 4 triangles are congruent and
in the kite there are two sets of congruent triangles. If we move the two triangles on the bottom of each quadrilateral
so that they match up with the triangles above the horizontal diagonal, we would have two rectangles.