#### Math - 2018-19

# 8.10 - Area and Perimeter

8.10The student willsolvearea and perimeter problems, including practical problems, involving composite plane figures.

*Adopted: 2016*

### 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**

·
8.10_{1}** 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.

·
8.10_{2}** 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.

·
8.10_{3}** 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

*Updated: Nov 20, 2018*