Question

Q4 please help thanks

Answer 1

see explanation

Explanation:

The area of the shaded triangle = area of ΔABD - area of ΔADC

A of ΔABD =
`(1)/(2)` × AD × BD

A =
`(1)/(2)` ×
`(√(2) )/(2)` ×
`(√(2) )/(2)`

=
`(2)/(8)` =
`(1)/(4)`

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A of ΔACD =
`(1)/(2)` × AD × DC

A =
`(1)/(2)` ×
`(√(2) )/(2)` ×
`(√(3) )/(3)`

A =
`(√(6) )/(12)`

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shaded area =
`(1)/(4)` -
`(√(6) )/(12)`

=
`(3)/(12)` -
`(√(6) )/(12)` =
`(3-√(6) )/(12)`

Answer 2

`\large\boxed{A==(3-\sqrt6)/(12)\ cm^2}`

Explanation:

The shaded region is the triangle with base b and height h.

`b=BD-CD\to b=(\sqrt2)/(2)-(\sqrt3)/(3)=(3\sqrt2)/((2)(3))-(2\sqrt3)/((2)(3))=(3\sqrt2-2\sqrt3)/(6)\\\\h=AD\to h=(\sqrt2)/(2)`

The formula of an area of a triangle:

`A=(bh)/(2)`

Substitute:

`A=((3\sqrt2-2\sqrt3)/(6)\cdot(\sqrt2)/(2))/(2)=\left((3\sqrt2-2\sqrt3)/(6)\right)\left((\sqrt2)/(2)\right)\left((1)/(2)\right)\\\\\text{use the distributive property}\ a(b+c)=ab+ac\\\\=((3\sqrt2-2\sqrt3)(\sqrt2))/((6)(2)(2))=((3\sqrt2)(\sqrt2)-(2\sqrt3)(\sqrt2))/(24)\\\\\text{use}\ √(a)\cdot√(a)=a\ \text{and}\ √(ab)=√(a)\cdot√(b)\\\\=((3)(2)-2\sqrt6)/(24)=(2(3-\sqrt6))/(24)=(3-\sqrt6)/(12)`