Question

all angles in the figure a right angles what is the total area of the square​

Answer 1

Given:

As in the diagram

To Find:

Total area of the square

Solution:

*See attached for labelling of the diagram

Find the area of C and D:

Area of C and D = 36 - 20

Area of C and D = 16 units²

Find the area of C:

Area of C = Area of D

Area of C = 16 ÷ 2

Area of C = 8 units²

It can be observed that:

Area of C = Area of D = Area of A = Area of F = 8 units²

Find the length of C:

C is a square

Length of C = √8 units

Find the area of B:

Area of B = 20 - Area of A

Area of B = 20 - 8

Area of B = 12 units²

Find the length of B:

Area = Length x Breath

12 = Length x √8

Length = 12 ÷ √8

Length = 3√2 units

Find the length of the big square:

Length of the big square = √8 + 3√2 + √8

Length of the big square =  7√2 units

Find the area of the big square:

Area = Length x Length

Area =  7√2 x  7√2

Area = 98 units²

Answer: The area of the square is 98 units.

Answer 2

The total area of the square​ is 98 unit²

Step-by-step explanation:

The area of A and B is:

A₁ = 36 = 20 = 16 unit²

The area of A is:

Aa = 16/2 = 8 unit²

Now,

∴ Area of A = Area of B = Area of G = Area of H = 8 unit²

The length of A is:

∴ La = √8

Area of D is:

Area of D = 20 - Area of G

Area of B = 20 - 8

∴ Area of B = 12 units²

Length of D is:

Area = Length × Breath

12 = Length × √8

∴ Length = 3√2 units

The length of the total square is:

Length = 7√2

The area of the total square is:

Area = 7√2 × 7√2

∴ Area = 98 units²