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Here are a few recommended readings before getting started with this lesson.
A diagonal of a rectangle divides the rectangle into two right triangles. Because of this, a formula for the area of a right triangle can be derived from the formula for the area of a rectangle. The good news is that the same formula applies to any type of triangle!
The area of a triangle is half the product of its base b and its height h.
A=21bh
The triangle's base can be any of its sides. The height – or altitude – of the triangle is the segment that is perpendicular to the base and connects the base or its extension with its opposite vertex.
A=21bh
On his birthday, Mark's uncle gave him a tangram, a Chinese puzzle made of seven polygons that can be used to create different shapes. The seven individual pieces are called tans.
Mark's uncle warned him that once the pieces are taken out of the box, putting them back is a challenge.
b=8, h=4
Multiply
ca⋅b=ca⋅b
Identity Property of Multiplication
Calculate quotient
Substitute values
ca⋅b=ca⋅b
Calculate quotient
LHS/2=RHS/2
Rearrange equation
Property | Justification |
---|---|
The opposite sides are congruent | Parallelogram Opposite Sides Theorem |
The opposite angles are congruent | Parallelogram Opposite Angles Theorem |
The diagonals bisect each other | Parallelogram Diagonals Theorem |
These properties are illustrated graphically in the next diagram.
The area of a parallelogram is equal to the product of its base b and height h. The base can be any side of the parallelogram and the height is the perpendicular distance to the opposite side.
Parallelograms can be divided into three main types: rectangles, rhombuses, and squares. It is the time to learn about rhombuses.
The area of a rhombus is half the product of the lengths of the diagonals.
Alternatively, since a rhombus is a parallelogram, its area can also be calculated by multiplying its base and height.
Since Mark received the tangram puzzle, he sees polygons everywhere.