Question

Find the area of the polygon. show your work

Answer 1

Look at the picture.

We have the triangle and the parallelogram.

The formula of an area of a triangle

$A_T=\dfrac{bh}{2}$

We have b = 5 and h = 3. Substitute:

$A_T=\dfrac{5\cdot3}{2}=\dfrac{15}{2}=7.5$

The fromula of an area of a parallelogram:

$A_P=bh$

We have b = 5 and h = 3. Substitute:

$A_P=5\cdot3=15$

The area of polygon:

$A=A_T+A_P\to A=7.5+15=22.5\ u^2$

--------------------------------------------------

Other method. (look at the second picture).

We have the three congruent triangles. The area of the polygon is equal three times the area of a one triangle.

$A_\Delta=\dfrac{bh}{2}$

b = 5, h = 3. Subsitute.

$A_\Delta=\dfrac{5\cdot3}{2}=\dfrac{15}{2}=7.5$

The area of the polygon:

$A=3A_\Delta\to A=3\cdot7.5=22.5\ u^2$