Question

A regular pentagon is divided into congruent triangles by drawing a line segment from each vertex to the center. Each triangle has an area of 24. What is the area of the pentagon

Answer 1

Area of pentagon
`ABCDE = 144 \ sq.unit`.

Explanation:

Labelled Diagram of given shape is shown below,

Given that,

A regular pentagon is divided into congruent triangle. each triangle has an area of
`24`
`sq.unit`.

So, Regular pentagon has an all sides are equal and all the corresponding angles are also equal. pentagon has an each angle measure is
`108`° and side says
`a \ unit`.

Here, According to Question

All triangles are congruent then there area will be same.

∴ area of pentagon
`ABCDE` = area of Δ
`AOB` + area of Δ
`BOC` + area of

Δ
`COD` + area of Δ
`DOE` + area of Δ
`EOA`.

=
`6* 24\ sq. unit` {Given that}

=
`144 \ sq.unit`

Hence,

Area of pentagon
`ABCDE = 144 \ sq.unit`.