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

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

ABCD is a parallelogram.

AD = 10, AB = 12. DE = 8W here  DE is perpendicular to AB.

To calculate the perimeter.

To calculate area .

Perimeter :

Since ABCD is a parallelogram, AB = CD = 12 and

AD = BC = 10.

So the perimeter AB+BC+CD+DA =  2(AB+AD) = 2(12+10) = 44 units.

The area of the parallelogram ABCB = AB*perpedicular DE = 12*8 =96 sq units.

william1941's profile pic

william1941 | College Teacher | (Level 3) Valedictorian

Posted on

In this problem we are given a that the  parallelogram ABCD has  AD=10, AB=12 and DE=8 where DE is perpendicular to AB.

Now take the triangle ADE, using the Pythagorean Theorem

AD^2= AE^2 + DE^2

=> AE^2 = 10^2 -8^2 = 100- 64 = 36

=> AE = 6

So EB = 6

Now lets draw a line BF that is perpendicular to DC and F lies on DC. We see that the ADE and CBF are congruent.

So we have two the parallelogram in three peices, 2 triangles and a rectangle. The area of the rectangle is 8*6 = 48 and that of the triangles is 2* (1/2) 6 * 8 = 48.

So the area of the parallelogram is 48+ 48 = 96. And the perimeter is 10*2+ 12*2 = 20 + 24 = 44.

The required area and perimeter are 96 and 44 resp.

Top Answer

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.

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