10.6.3 Tangram Areas Again
Activity: Tangram Areas Again
The figure below shows a 4 cm square tangram puzzle.
Note that the image on your monitor may not be drawn to scale.
By using the formulas for the area of a triangle and for the area of a parallelogram, calculate the areas of the following shapes.
Check that your answers agree with those you obtained by counting the squares.
(a) with AD as the base
(a) . The perpendicular height from F onto . The area of a triangle =
So the area of .
How many other ways could you calculate this area? Think about what information you have about the whole space.
(b) with DH as the base
(b) . The perpendicular height from E onto . So, the area of .
(c) Parallelogram GBJI with BJ as the base
(c) . The perpendicular height from G onto .
That means the area of .
(d) The base and the corresponding height . So, the area of .
Many area problems can be calculated by using combinations of squares, rectangles, and triangles. However, you often need to find circular areas, too. The formula for the area of a circle is:
We will look at more on this on the next page.
Now that you know how to calculate the areas of basic shapes, you can calculate more complicated areas by breaking each shape into basic shapes and adding the individual areas.
Even the surface areas of some containers that have curved surfaces like cylinders can be broken down into circles and rectangles. [ How would you find the surface area of a box or a cylinder? For the cylinder, think about what shape you would get if you unrolled the tube. ]