Math - 2018-19
8.10 - Area and Perimeter
8.10 The student will solve area and perimeter problems, including practical problems, involving composite plane figures.
BIG IDEAS
- I can figure how much paint will cover walls and ceiling of
a room, how much tile will cover all the floors in a house, how much fence is
required for a garden, and how far it is to run around the school property.
- I will employee the concept of a
whole is the sum of its parts by dividing compound figures into regular
polygons to apply area and perimeter formulas.
UNDERSTANDING THE STANDARD
· A plane figure is any two-dimensional shape that can be drawn in a plane.
· A polygon is a closed plane figure composed of at least three line segments that do not cross.
· The perimeter is the path or distance around any plane figure. The perimeter of a circle is called the circumference.
· The area of a composite figure can be found by subdividing the figure into triangles, rectangles, squares, trapezoids, parallelograms, circles, and semicircles, calculating their areas, and combining the areas together by addition and/or subtraction based upon the given composite figure.
· The area of a rectangle is computed by multiplying the lengths of two adjacent sides (A = lw).
· The area of a triangle is computed by multiplying the measure of its base by the measure of its height and dividing the product by 2 or multiplying by (A or A ).
· The area of a parallelogram is computed by multiplying the measure of its base by the measure of its height (A = bh).
· The area of a trapezoid is computed by taking the average of the measures of the two bases and multiplying this average by the height (.
· The area of a circle is computed by multiplying pi times the radius squared ().
· The circumference of a circle is found by multiplying pi by the diameter or multiplying pi by 2 times the radius ( or ).
· The area of a semicircle is half the area of a circle with the same diameter or radius.
ESSENTIALS
- How does knowing the areas of polygons assist in
calculating the areas of composite figures?
The area of a composite figure can be found by subdividing the figure into triangles, rectangles, squares, trapezoids and semi-circles, calculating their areas, and adding the areas together.
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
·
8.101 Subdivide
a plane figure into triangles, rectangles, squares, trapezoids, parallelograms,
and semicircles. Determine the area
of subdivisions and combine to determine the area of the composite
plane figure.
·
8.102 Subdivide
a plane figure into triangles, rectangles, squares, trapezoids, parallelograms,
and semicircles. Use the attributes
of the subdivisions to determine the
perimeter of the composite plane figure.
·
8.103 Apply
perimeter, circumference, and area formulas to solve practical problems involving composite plane figures.
KEY VOCABULARY
composite figure, triangle, rectangle, square, trapezoid, semicircle,
perimeter, circumference