Find the area of a figure formed by joining the midpoints of the adjac

1.	Find the area of a figure formed by joining the midpoints of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm.
Answer» We know that ABCD is a rhombus with P, Q, R and S as the midpoints of AB, BC, CD and DA. AC and BD diagonals are joined. Using the midpoint theorem We know that PQ = ½ AC By substituting the values we get PQ = ½ (16) By division PQ = 8cm In △ DAC we know that S and R are the midpoints of AD and DC Using the midpoint theorem SR = ½ AC By substituting the values SR = ½ (12) By division SR = 6cm Consider the rectangle PQRS Area of the rectangle PQRS = length × breadth So we get Area of the rectangle PQRS = 6 × 8 By multiplication Area of the rectangle PQRS = 48 cm² Therefore, area of the figure is 48 cm².

Find the area of a figure formed by joining the midpoints of the adjacent sides of a rhombus with diagonals 12 cm and 16 cm.

Answer»

We know that ABCD is a rhombus with P, Q, R and S as the midpoints of AB, BC, CD and DA.

AC and BD diagonals are joined.

Using the midpoint theorem

We know that

PQ = ½ AC

By substituting the values we get

PQ = ½ (16)

By division

PQ = 8cm

In △ DAC we know that S and R are the midpoints of AD and DC

Using the midpoint theorem

SR = ½ AC

By substituting the values

SR = ½ (12)

By division

SR = 6cm

Consider the rectangle PQRS

Area of the rectangle PQRS = length × breadth

So we get

Area of the rectangle PQRS = 6 × 8

By multiplication

Area of the rectangle PQRS = 48 cm²

Therefore, area of the figure is 48 cm².