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:

$tan(\angle C)=\frac{DP}{CP}$

$tan(45^{\circ})=\frac{5}{CP}$

$\therefore CP=\frac{5}{tan(45^{\circ})}=\frac{5}{1}=5$

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 $\Delta ADE$,

$tan(\angle D)=\frac{AE}{DE}$

$tan(45^{\circ})=\frac{AE}{10}$

$\therefore AE=10\times tan(45^{\circ})=10\times 1=10$

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

Area=$\frac{1}{2}$ x base x height =$\frac{1}{2}\times 10\times 10=50$ square units