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Question
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is ______.
Options
a rhombus of area 24 cm2
a rectangle of area 24 cm2
a square of area 26 cm2
a trapezium of area 14 cm2
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Solution
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is a rhombus of area 24 cm2.
Explanation:
Given: Rectangle with sides 8 cm and 6 cm
To find: Area of the figure which is formed by joining the midpoints of the adjacent sides of rectangle.
Calculation: Since we know that area of rhombus = `1/2 (d_1 xx d_2)`
For rhombus EFGH, EG is the one diagonal which is equal to DA
FH is the other diagonal which is equal to AB
Area of rhombus = `1/2 (d_1 xx d_2)`
Area of rhombus = `1/2 ( 8 xx 6)`
Area of rhombus = `1/2 (48)`
Area of rhombus = 24 cm2
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