A trapezium with 3 equal sides and one side double the equal side can be divided into __________ equilateral triangles of _______ area.
Solution:
The diagram below shows a Trapezium ABCD with three sides equal and fourth side twice the other sides.
ABE
E is the midpoint of the side AD which is twice the other three sides. Hence
CE = BE = L.
Therefore we get three equilateral triangles
△ABE, △BEC and △ECD
The areas of all the triangles are equal as they are equilateral.
✦ Try This: The area of the rhombus is a parallelogram with all sides ____________ and its area is equal to the half of the product of its ____________.
A rhombus is a parallelogram with the following properties:
1) All sides equal
2) Diagonals which are equal and bisect each other at right angles
3) Opposite angles are equal
The area of the rhombus is equal to the sum of all the four triangles △AOB, △BOC, △DOC and △AOD. Their sum can be expressed as :
Area of rhombus(A) = 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2)
Area of Rhombus(A) = 4 × (xy/8) = xy/2
The length of one diagonal = x
The length of the other diagonal = y
Since the Area of the Rhombus(A) as calculated above is xy/2 we can state:
Area of rhombus = 1/2× (Product of the diagonals x and y)
Therefore,
The area of the rhombus is a parallelogram with all sides equal and its area is equal to the half of the product of its diagonals.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 40
A trapezium with 3 equal sides and one side double the equal side can be divided into __________ equilateral triangles of _______ area.
Summary:
A trapezium with 3 equal sides and one side double the equal side can be divided into three equilateral triangles of equal area
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