Question

find the area of BEF in a square ABCD and area of BEC is equal to 3, area of EFD is equal to 5 and area of BFA is equal to 4​

Answer 1

THE QUESTION ASKED IS WRONG FOR EXPLANATION SEE ATTACHED IMAGE

Answer 2

Answer:

The Area Δ BFE is 11.04 unit²

Step-by-step explanation:

Given as :

From the figure

Let The each side of square ABCD = x unit

i.e BA = AD = DC = CB = x unit

Area  Δ BAF = 4 unit²

Area  Δ EDF = 5 unit²

Area  Δ BCE = 3 unit²

Let FD = ED = CE=  y unit

So, AF = ED = x - y unit

In Δ BAF

Area  Δ BAF = $\dfrac{1}{2}$ × BA × AF

Or, 4 × 2 = x × (x - y )

Or, x² - x y - 8 = 0                  ...........A

Again

Area  Δ EDF =  $\dfrac{1}{2}$ × FD × ED

Or, 5 = $\dfrac{1}{2}$ × FD × ED

or, $\dfrac{1}{2}$ × y × y = 5

Or, y² = 10

∴  y = √10                               .............B

Now, from eq A and eq B

x² - x × √10 - 8 = 0

Solving the quadratic equation

x = 4.8 , - 1.6

Or, x = 4.8

So, The measure of side AD = AF + FD

i.e AD = x - √10 + √10

Or, AD = 4.8 + 0

So, AD = 4.8 unit

i,e each side of square = 4.8 unit

Now,

Area of square ABCD = side × side

Or, Area of square ABCD = 4.8 unit × 4.8 unit

∴  Area of square ABCD = 23.04 unit²

So, Area Δ BFE = Area of square ABCD - ( Area Δ BAF + Area Δ FDE + Area Δ BCE )

or,  Area Δ BFE = 23.04 unit² - (4 unit² + 5 unit² + 3 unit² )

Or, Area Δ BFE = 23.04 unit² - 12 unit²

∴ Area Δ BFE = 11.04 unit²

Hence, The Area Δ BFE is 11.04 unit²  Answer