Answer:
Area of pentagon [tex]ABCDE = 144 \ sq.unit[/tex].
Step-by-step 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 [tex]24[/tex][tex]sq.unit[/tex].
So, Regular pentagon has an all sides are equal and all the corresponding angles are also equal. pentagon has an each angle measure is [tex]108[/tex]° and side says [tex]a \ unit[/tex].
Here, According to Question
All triangles are congruent then there area will be same.
∴ area of pentagon [tex]ABCDE[/tex] = area of Δ[tex]AOB[/tex] + area of Δ[tex]BOC[/tex] + area of
Δ[tex]COD[/tex] + area of Δ[tex]DOE[/tex] + area of Δ[tex]EOA[/tex].
= [tex]6\times 24\ sq. unit[/tex] {Given that}
= [tex]144 \ sq.unit[/tex]
Hence,
Area of pentagon [tex]ABCDE = 144 \ sq.unit[/tex].
