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Chapter 10: Problem 54

Using the formula for the area of a parallelogram \((A=b h)\), explain how the formula for the area of a triangle \(\left(A=\frac{1}{2} b h\right)\) is obtained.

Short Answer

Expert verified
The formula for the area of a triangle \( \ A = \frac{1}{2}bh \) is obtained by cutting a parallelogram in half along its diagonal, leaving us with two equal triangles.

Step by step solution

01

Understanding the parallelogram

A parallelogram is a four-sided figure (or a quadrilateral) where opposite sides are parallel and equal in length. And the formula to find the area of parallelogram is \(A=bh\) where 'b' is base (the length of any side) and 'h' is height (the vertical distance from the base to the opposite top vertex).
02

Understanding the triangle

A triangle can be considered half of a parallelogram when the latter is divided along a diagonal. When it comes to a triangle, it consists of three sides and the base and height can be any side and the perpendicular distance to that side from the opposing vertex respectively.
03

Deriving area formula of triangle from parallelogram

When we cut the parallelogram along one of its diagonals, we get two triangles. It is clear that the total area of the triangles (2) is equal to the area of the parallelogram. Thus, the area of one triangle is half of the area of the parallelogram. Hence, the formula for the area of a triangle is derived: \(\ A = \frac{1}{2}bh\).

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