Parallelograms & Triangles between Parallels | Solved Examples

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• Parallelograms & Triangles between Parallels | Solved Examples

If the area of ∆DEC is 6.99 cm² , find the area of ∆ABC.

Solution

We are going to compare the triangles in the diagram to ∆DEC. We are not given a parallel line in the question, so we are going to use equal bases and perpendicular height in our calculations.

The two dashes and single dash represent equal length.

∴ \( \scriptsize \overline{AE} = \scriptsize \overline{EC} \)and \( \scriptsize \overline{DC} = \scriptsize \overline{DB} \)

Choose \( \scriptsize \overline{CE} \)to be the base of triangle ∆DEC, we get the following.

Remember: We use the perpendicular height when calculating the area of a triangle.

The perpendicular height, h of ∆DEC is \( \scriptsize \overline{DF} \)as shown below.

∴ Area of ∆DEC = \( \frac{1}{2} \scriptsize \: \times \:(EC)(DF) \)

Comparing ∆DEC to ∆DAE, we can see that they have a common base , since \( \scriptsize \overline{AE} = \scriptsize \overline{EC} \)and a common perpendicular height, h.

Note: If we move \( \scriptsize \overline{DF} \)to any point on \( \scriptsize \overline{AC} \), the perpendicular height will be the same for ∆DEC and ∆DAE, as