Question 4 of 14intermediate🔧 ApplyLong Answer3 marks

Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral.

Correct Answer

Method to Obtain a Quadrilateral with Half the Area:

Step 1: Take quadrilateral ABCD.

Step 2: Find midpoints E, F, G, H of sides AB, BC, CD, DA respectively.

Step 3: Join EFGH to form a new quadrilateral.

Step 4: The area of EFGH = ½ × Area of ABCD.

Alternative Method:

Draw a diagonal to divide ABCD into two triangles.

Find the midpoint of the diagonal.

Join the midpoint to two opposite vertices to create a quadrilateral of half the area.

Answer: The quadrilateral formed has exactly half the area of the original quadrilateral.

Exercise: Figure it Out (Section 3) | Q: 5 | (Page Page 13)
For More Understanding

Explanation

The chapter discusses how the line joining a vertex to the midpoint of the opposite side divides a triangle into two equal areas. This principle can be extended to quadrilaterals by using midpoints of sides or diagonals.

Solution Steps

  1. Take quadrilateral ABCD.

  2. Find midpoints E, F, G, H of sides AB, BC, CD, DA respectively.

  3. Join EFGH to form a new quadrilateral.

  4. The area of EFGH = ½ × Area of ABCD.

  5. Alternative: Draw a diagonal to divide ABCD into two triangles.

  6. Find the midpoint of the diagonal.

  7. Join the midpoint to two opposite vertices to create a quadrilateral of half the area.

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