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Maths 3 Mark Question

Quadrilaterals · Maharashtra Board STD 6 (MSBSHSE - English Medium). 4 questions.

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3 Mark Question

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Question 13 Marks
What is a trapezium? When do you call a trapezium an isosceles trapezium? Draw an isosceles trapezium. Measure its side and angles.
Answer

A trapezium has only one pair of parallel sides.
A trapezium is said to be an isosceles trapezium if its non-parallel sides are equal.
Following are the measures of the isosceles trapezium:
AB = 5.4cm
BC = 3cm
DC = 7.4cm
AD = 3cm
$\angle\text{A}=\angle\text{B}=110^{\circ}$
$\angle\text{D}=\angle\text{C}=70^{\circ}$
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Question 23 Marks
Two sides of a parallelogram are in the ratio 4 : 3. If its perimeter is 56cm, find the lengths of its sides.
Answer
Two sides of a parallelogram are in the ratio 4 : 3.
Let the two sides be 4x and 3x.
In a parallelogram, opposite sides are equal and parallel. So, they are also in the ratio of 4 : 3, i.e. 4x and 3x.
Perimeter = 4x + 3x + 4x + 3x
⇒ 56 = 14x
⇒ x = 5614
⇒ x = 4
Therefore, 4x = 16 and 3x = 12
Lengths of its sides are 16cm, 12cm, 16cm and 12cm.
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Question 33 Marks
In the adjacent figure, a quadrilateral has been shown.
Name:
  1. Its diagonals.
  2. Two pairs of opposite sides.
  3. Two pairs of opposite angles.
  4. Two pairs of adjacent sides.
  5. Two pairs of adjacent angles.
Answer
  1. The diagonals are AC and BD.
  2. AB and CD, and AD and BC are the two pairs of opposite sides.
  3. $\angle\text{A}$ and $\angle\text{C},$ and $\angle\text{B}$ and $\angle\text{D}$ are the two pairs of opposite angles.
  4. AB and BC, and AD and DC are the two pairs of adjacent sides.
  5. $\angle\text{A}$ and $\angle\text{B},$ and $\angle\text{C}$ and $\angle\text{D}$ are the two pairs of adjacent angles.
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Question 43 Marks
Draw a parallelogram ABCD in which AB = 6.5cm, AD = 4.8cm and $\angle\text{BAD}=70^{\circ.}$ Measure its diagonals.
Answer
Since ABCD is a parallelogram, AB = DC = 6.5cm and AD = BC = 4.8cm. Given:$\angle\text{A}=70^{\circ}$
Steps of construction:
  1. Draw AD equal to 4.8cm.
  2. Make an angle of 70° at A and cut an arc of 6.5cm. Name it B.
  3. Cut an arc of 4.8cm from B and 6.5cm from D. Name it C.
  4. Join AB, BC and CD.
  5. Measuring the diagonal AC and BD, we get AC equal to 9.2cm and BD equal to 6.6.cm.
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