Math, asked by weeb32, 6 months ago

find the perimeter and area of the adjoining figure in being given that AB is parallel to CD ab = 12 CM CD = 15 cm and BD = 4 cm and one end of the figure is a semicircle with BD as diameter .(take Pi =3.14)​

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Answers

Answered by SujalSirimilla
26

NICE QUESTION!

GIVEN:

  • AB = 12 cm.
  • CD = 15 cm.
  • BD = 4 cm.
  • BD is the diameter of the semicircle ◠BD. Thus, radius = ½Diametre, i.e., radius = ½×4 = 2 cm.
  • AB║CE.

CONSTRUCTION:

  • Draw BE║AC [It is already drawn in the figure]. Then, we can see that if BE║AC and AB║CE, ABEC is a ║gm. [In case you didn't know, ║gm is a symbol for a parallelogram].

SOLUTION:

PERIMETER:

Now, CD is 15 cm. And CE is 12 cm because AB=CE [ABCD is a ║gm and opposite sides of a parallelogram are equal] and AE=12 cm.

We know that CE+ED=CD. [CD=15 cm, CE=12 cm.]

12+ED=15

ED=15-12

ED=3cm.

Since BD is a diameter, It is perpendicular to the base. In other words, BD⊥CD. Thus, BD can be considered the height of ΔBDE, ΔBDE is a right-angled triangle.

We can use Pythagoras theorem:

BE²=BD²+ED²

BE²=4²+3²

BE²=16+9

BE²=25

BE=√25

BE=5cm.

Here, BE=AC because ABEC is a ║gm and opposite sides of a ║gm are equal.

∴ AC=5cm.

Then,

We know that the circumference of a semicircle is (πr)

Radius=2 cm,

π=3.14.

Circumference (BD) = 2×3.14 = 6.28 cm.

Now, we know BD=6.28 cm, CD=15cm, AC=5cm, AB=12cm.

Add them to get the perimeter.

Perimeter = 6.28+15+5+12 = 38.28 cm.

AREA:

Now, consider trapezium ABDC.

Since BD is a diameter, It is perpendicular to the base. In other words, BD⊥CD. Thus, BD can be considered the height of ABDC.

Area of trapezium = ½(sum of ║ sides)×(height)

Ar(ABDC)=½(12+15)(4)

Ar(ABDC)=½(108)

Ar(ABDC)=54 cm².

Then, Area of semicircle=½×(πr²)

Radius=2, π=3.14

Ar(BD)=½×3.14×2²

Ar(BD)=6.28cm².

Total area = Area of the semicircle + area of the trapezium

A = (6.28+54) cm²

A = 60.28 cm²

CONCLUSION:

  • Area = 60.28 cm²
  • Perimeter = 38.28 cm.

THANK YOU (^▽^)

HOPE THIS HELPS :D

Answered by miraculousnidhi64
2

we have to add all the areas according to their formulas

Then the perimeter of the semicircle and add all the boundaries of the figure

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