Question

How to find the area

Answer 1

You multiply length times width or base times height.

Answer 2

For a complete understanding of the question please find the diagram in the file attached.

In the diagram a perpendicular DP is dropped from D on AB as shown.

It is given that
`\angle A=45^(\circ)` and that
`\angle B=90^(\circ)`. Thus, the
`\angle C=45^(\circ)`. This is because we know that the interior angles of any triangle add up to make
`180^(\circ)`.

Thus,
`\Delta CDP` gives:

`tan(\angle C)=(DP)/(CP)`

`tan(45^(\circ))=(5)/(CP)`

`\therefore CP=(5)/(tan(45^(\circ)))=(5)/(1)=5`

Thus, PB=CB-CP=15-5=10

Now, since,
`DE\parallel CB`, then by corresponding angles,
`\angle D=45^(\circ)`

Also, we note that DE=PB=10

Thus, in
`\Delta ADE`,

`tan(\angle D)=(AE)/(DE)`

`tan(45^(\circ))=(AE)/(10)`

`\therefore AE=10* tan(45^(\circ))=10* 1=10`

Thus, now to find the area of the triangle
`\Delta ADE` all that we have to do is use the Area formula as:

Area=
`(1)/(2)` x base x height =
`(1)/(2)* 10* 10=50` square units