What does tiling a two-dimensional region involve?
Covering it with copies of the same shape or shapes without gaps or overlaps.
What do figures that fit exactly on top of one another have in common?
They have the same area.
How can a figure’s area be found by rearranging its pieces?
Find the areas of the rearranged known shapes and add them.
How can a figure’s area be found using a containing shape?
Subtract the missing piece’s area from the containing shape’s area.
What defines a parallelogram’s opposite sides?
They are parallel and equal in length.
What relationship do a parallelogram’s opposite angles have?
They have equal measures.
How can rearranging a parallelogram help find its area?
Decompose and rearrange it into a rectangle.
Which side of a parallelogram can be chosen as its base?
Any side.
How is a parallelogram’s height measured from its base?
As the length of a perpendicular segment from the base to the opposite side.
What is the area formula for base and corresponding height ?
What does a diagonal joining opposite vertices do to a parallelogram?
It divides it into two identical triangles.
What can two identical copies of any triangle form when joined along matching sides?
A parallelogram.
What is the area formula for a triangle with base and corresponding height ?
Which sides of a triangle can be chosen as its base?
Any of its three sides.
How is a triangle’s height corresponding to a base measured?
As the length of a perpendicular segment from the base or its extension to the opposite vertex or a parallel line through it.
What is a polygon?
A two-dimensional figure made of straight segments whose sides do not cross.
Where are the vertices of a polygon located?
At the points where its segments connect.
What does the area of a polygon measure?
The region enclosed by the polygon.
How can a polygon’s area be found using triangles and rectangles?
Decompose its interior into triangles and rectangles, then add their areas.
How can an enclosing rectangle be used to find a polygon’s area?
Subtract the areas of corner triangles from the rectangle’s area.
What does surface area measure?
The number of unit squares needed to cover an entire surface without gaps or overlaps.
How is the surface area of a flat-faced three-dimensional figure calculated?
By summing the areas of all its faces.
What is a net of a polyhedron?
A two-dimensional arrangement of polygons that forms its faces and can be folded into a model.
How can a polyhedron’s surface area be found from its net?
Calculate the area of every face and add the face areas.
What faces form a polyhedron?
Polygonal faces.
How do a polyhedron’s faces meet?
Along complete edges.
What two features define a prism’s bases?
They are identical and parallel.
What shapes can connect a prism’s bases?
Rectangles or parallelograms.
Where do a pyramid’s triangular faces meet?
At a single vertex.
What dimensional attribute does length measure?
A one-dimensional attribute.
What dimensional attribute does area measure?
A two-dimensional attribute.
What dimensional attribute does volume measure?
A three-dimensional attribute.
How can two figures’ volumes and surface areas differ?
They can share volume but differ in surface area, or share surface area but differ in volume.
What does an exponent indicate about a number?
How many times the number is multiplied by itself.
What operation does squaring a number mean?
Multiplying it by itself.
What operation does cubing a number mean?
Multiplying it by itself three times.
What is the surface area of a cube with edge length ?
.
Why is a cube’s surface area six times the area of one face?
A cube has six identical square faces.
How can comparing plane-covering patterns help begin area reasoning?
It shows which patterns cover more of the plane.
In what units is area measured?
Square units.
What unit measures the area of a rectangle with side lengths in centimeters?
Square centimeters.
What is the area of each equal triangle formed by decomposing a square of area one square unit?
One-half square unit.
What area does the larger triangle have when formed from two squares of area one square unit?
Two square units.
What is the area of a parallelogram with base 6 units and height 4 units?
24 square units.
What determines equal areas for parallelograms with different shapes?
The same base and corresponding height.
What can joining identical triangles along different matching sides produce?
Different parallelograms.
What is the area of a triangle with base 5 units and height 6 units?
15 square units.
In a right triangle, which sides can serve as a base and its corresponding height?
The two perpendicular sides.
How do a polygon’s numbers of vertices and sides compare?
They are equal.
What is a face of a three-dimensional figure?
A flat side.
What is the surface area of a rectangular prism with edges 2 cm, 3 cm, and 4 cm?
52 square centimeters.
What determines the name of a prism or pyramid?
The shape of its base.
How many square faces does a cube have?
Six.
In a folded cube net, what happens to each square’s edges?
They join edges of other squares.
What volume do the specified 1 × 2 × 2 cm and 1 × 1 × 4 cm prisms share?
4 cubic centimeters.
What surface area does the 1 cm by 2 cm by 2 cm prism have?
16 square centimeters.
What surface area does the 1 cm by 1 cm by 4 cm prism have?
18 square centimeters.
What is the area of a square with side length 5 inches?
25 square inches.
What is the volume of a cube with edge length 4 cm?
64 cubic centimeters.
Answer 30 questions on Area and Volume Geometry.
1. What does it mean to tile a two-dimensional region?
2. A student wants to begin investigating which of two patterns covers more of a plane. What is a useful first approach?
Go over the full study guide for Area and Volume Geometry.
Read the study guide →Upload your class notes and Revizly writes your flashcards in about a minute.
Flashcard maker