Calculate the perimeter and the area of the paralelogram ABCD if AD=10, AB=12, DE=8. DE is perpendicular to AB.

In a parallelogram, the opposite sides are parallel and
equal.

AB = CD =
12

and

BC = AD =
10

The perimeter of a geometric shape is the sum of the
lengths of the sides of that shape.

P =
AB+BC+CD+AD

Since AB = CD and BC = AD, we could re-write
the perimeter as:

P =
2(AB+BC)

P = 2(12+10)

P =
2*22

P = 44 units

The area of
the parallelogram could be written as a sum of 2 triangles and a
rectangle.

A = 2*A(AED) +
A(DEBF)

To calculate the area of AED, we need to calculate
the cathetus AE. We'll use the Pythagorean theroem:

AE^2 =
AD^2 - DE^2

AE^2 = 100-64

AE^2
= 36

AE = 6

Area of AED =
AE*ED/2

Area of AED =
6*8/2

Area of AED = 24 square
units

To calculate the area of the rectangle DEBF, we'll
calculate first the width EB.

EB =
AB-AE

EB = 12-6

EB =
6

Area of DEBF = EB*DE

Area of
DEBF = 6*8

Area of DEBF = 48 square
units

The area of ABCD
is:

A(ABCD) = 2*A(AED) +
A(DEBF)

A(ABCD) = 2*24 +
48

A(ABCD) =
2*48

A(ABCD) = 96 square
units.