Question

ABCD is a parallelogram what is the area of ABCD?

Answer 1

Answer:

Area of parallelogram = 432 $cm^2$.

Length of $\overline{AC}$= 48 cm.

Step-by-step explanation:

In the given figure I ABCD is a parallelogram

Base of parallelogram ABCD= AB=18 cm

Length of side BC= 30 cm

We know that

area of parallelogram= $base\times height$

Pythogorous theorem :

$(perpendicular\; side)^2+ (Base)^2= ( hypotenuse)^2$

$(BC)^2= (AB)^2+ (AC)^2$

$(30)^2=(18)^2+ (AC)^2$

900=324+$(AC)^2$

$(AC)^2$=900-324=576

AC=$\sqrt{576}$=24 cm

Length of side AC=24 cm

Area of parallelogram = $18\times 24$=432 $cm^2$.

In II figure

AD=26 cm

DB=10 cm

AB=BC ( given)

By using pythogorous theorem

In triangle ABD

$(AD)^2= (BD)^2+ (AB)^2$

$(26)^2= (10)^2+ (AB)^2$

676=100 +$(AB)^2$

$(AB)^2$= 676-100=576

AB=$\sqrt{576}$

AB=24 cm

AC= $2\times AB$

AC= $2\times 24$

AC=48 cm .