Question

In a right-angled Δ ABC. D is the mid-point of AB and F is the mid-point of AD. Given that AG // DE // BC and the area of the triangle is 36 cm2, find the area of the trapezium FGED.

​

Answer 1

Step-by-step explanation:

I you should check the question at once .plzz

Answer 2

In a right angle triangle ABC. D is the midpoint of AB and F is the midpoint of AD. Given that AG||DE||BC|| and the area of the triangle is 36cm^2. The area of trapezium FGED is 6.75cm^2.

Stepwise explanation is given below:

- It is given that the

FG||DE||BC||

- In the ΔABC and ΔADE

Angle ADE = Angle ABC...( Each 90°)

Angle AED = angle ACB..(corresponding angle)

- By A.A. criteria Δ ABC is congurent to Δ ADE

Area(ADE)/area(ABC)=(AD/AB)^2...(by theoram)

Area (ADE)/area(ABC)=(AD/2AD)^2......(as D is the midpoint)

Area (ADE)/36=(1/2)^2

Area (ADE)=1/4*36=36/4

Area (ADE)=9 cm^2

- Now, in ΔADE and ΔAFG

Angle AFG = Angle ADE...( Each 90°)

Angle AGF = angle AED..(corresponding angle)

- By A.A. criteria Δ ADE is congurent to Δ AFG

Area(AFG)/area(ADE)=(AF/AD)^2...(by theoram)

- Area (AFG)/area(ADE)=(AF/2AF)^2......(as F is the midpoint)

Area (AFG)/9=(1/2)^2

Area (AFG)=1/4*9=9/4

Area (AFG)=2.25 cm^2

- Now, we need the area of FGED

Area (FGED)= Area (ADE) - Area (AFG)

Area (FGED)= 9 cm^2 - 2.25 cm^2

Area (FGED) = 6.75 cm^2