Area and Volume
Honors Geometry Unit 9
Warm Up for 4/10
• A room has measurements of 15 feet by 20 feet
• What is the perimeter around the room?
• What is the area of the room?
• If another room has measurements of 11 feet and 24 feet, which
has the bigger perimeter? Area?
Perimeter
• Length around a polygon
• Found by adding up the lengths of all sides
• No formula to remember, simply add up the sides
Area
• Area is the number of square units covered by a shape.
• Area is a measure of size, not length
• Use square units to measure
• Area for each shape is found using different formulas
Area
Area
• With polygons, the height is always perpendicular to the base
• Can be found using a perpendicular segment either inside or
outside of the figure
• No matter what the shape looks like, parallelograms with the same
base and height measurements will have the same area
Triangle Area
• Any parallelogram can be divided into two congruent triangles, each
with the same base and height
• Therefore, the area of a single triangle is equal to half of the
parallelogram with the same base and height
Triangle Areas
• It doesn’t matter which side is the base, as long as the height is
perpendicular to it
Area
Area
Warm Up of 4/11
Area of a Trapezoid
• To find the area of a trapezoid, we need to think about it as a
rectangle
Area of a Trapezoid
• Find the area of each trapezoid
Area of Rhombuses/Kites
• We can use rectangles to find the area of rhombuses and kites too
Area of Rhombuses/Kites
• Find the area of each rhombus/kite
Bell Work for 4/12
• Find the area of each figure
Area
• In order to solve the area of the shapes we have looked at so far,
we must use different formulas for each
• Parallelogram
Triangle
Trapezoid
Rhombus/Kite
• For any Regular Polygon, though, we can use the same formula
• We just have to account for the number of sides in each polygon
Regular Polygons
• Regular Polygons:
• They are polygons that have
• Names for polygons:
Regular Polygons
• We need 2 new terms to refer to
parts we need on the polygons:
• Radius: Distance from the
center to each vertex
• Apothem: Distance from the
center to the midpoint of
each side
• Perpendicular to the side
• All radii are congruent and all
apothems are congruent
Area
• Using the radii and apothems, we can divide any n-gon into n
congruent triangles
• Any figures that are congruent have the same area, so all of those triangles
have the same area
• Area of each triangle:
• Total Area:
Warm Up for 4/17
Find the Area of Each Figure
Find the Area of Each Figure
Warm Up for 4/18
• Find the area of each polygon to the nearest hundredth.
Circles
• A circle is a set of all points equidistant from a center point.
• Radius–
• Diameter—
• Area & Circumference—
Circles
• Find the circumference and area of each circle
Circles
• Central Angle—
Circles
• Arc—Part of a circle’s circumference that relates to a central angle
• Semicircle—
• Minor Arc—
• Major Arc—
Arcs
Warm Up for 4/19
Arcs
Arcs
Arcs
Circles
Circles
Circles
Warm Up for 4/20
Circles
Circles
• Find the area of the shaded regions.
• Find the area of the shaded regions.
Warm Up for 4/21
• The two polygons are similar. If the area of the smaller one is 25 cm2,
what is the area of the larger one.
Bell Work for 5/9
Surface Area
• We can use what we know about the areas of 2-Dimensional shapes
to find the surface areas required to make 3-Dimensional Solids
• Face:
• Edge:
• Vertex:
• Surface Area: