# 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

2016 VDOE Curriculum Framework - 8.10 Understanding

·  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

Updated: Nov 20, 2018