Question

ABCD is a square of side 12 cm. It is formed from two rectangles AEGD and

EBCG. H is a point on AD and F is a point on BC.
Find the area of EFGH.

Answer 1

Answer:72
`cm^(2)`

Solution 1:

Step 1: Find EF use Pythagorean theorem

`EF^(2) = EB^(2) + BF^(2)`

`EF^(2) = 6^(2) + 6^(2)`

EF =
`\sqrt{6^(2) + 6^(2) }` = 6
`√(2)` cm

Step 2: The area of EFGH =
`EF^(2)`=
`(6√(2) )^(2)` = 72

Solution 2: See that the area of EFGH is equal
`(1)/(2)` the area of ABCD

The area of ABCD = 12x12 = 144

Thus, the area of EFGH = 144: 2 = 72:)

Have a nice day!