Bissoy.com
Doctors Medicines MCQs Q&A

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in square cm) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?

Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in square cm) of an equilateral triangle with side equal to the bigger diagonal of the rhombus? Correct Answer 12√3

Given:

Length of each side = 4 cm = length of smallest diagonal

Concept used:

Diagonals of the rhombus bisect each other.

Also, diagonals are perpendicular to each other.

Calculation:

Let the longest diagonal be d.

42 = 22 + (d/2)2

16 - 4 = d2/4

12 × 4 = d × d 

d = 4√3

Side of the equilatral triangle = 4√3

Area of the triangle = (√3/4) × a2 = (√3/4) × (4√3) × (4√3)

Area of the triangle = 12√3 cm2.

∴ The area of the triangle is 12√3 cm2.

Related Questions

The smaller diagonal of a rhombus is equal to the length of its sides. If the length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with side equal to the bigger diagonal of the rhombus?
Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 6 cm, then what is the area (in cm2) of an equilateral triangle whose side is equal to the bigger diagonal of the rhombus?
Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 6 cm, then what is the area (in sq.cm) of an equilateral triangle whoseside is equal to the bigger diagonal of the rhombus?
There is a rhombus of side 6 cm. One of the diagonal of the rhombus is equal to the side of the rhombus. An isosceles triangle is formed whose two equal sides are equal to another diagonal of the rhombus and the third side is equal to 8 cm. Find the area of the triangle.
Smaller diagonal of a rhombus is equal to length of its sides. If length of each side is 4 cm, then what is the area (in cm2) of an equilateral triangle with sideequal to the bigger diagonal of the rhombus?
Which of the following statements is/are true? A: If the sides of an equilateral triangle becomes 2√2 times, then its area will become 4√6 times. B: If the distance between any two parallel sides of a rhombus is 25% less than its diagonal, then its other diagonal will be 50% more than its side. C: If ratio between altitude and base of a right-angled triangle is 3: 5, then the ratio between its hypotenuse and base will be √30: 5.
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
A person walks along edge of a square park of side 20 m covering two sides then start walking on diagonal till he covers 1/4th distance of whole diagonal and then starts walking on path of smaller square field. Then he covers two sides and again starts walking on diagonal of bigger Square Park. Then find distance covered by him? (Take value of √2 = 1.4)
Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is:
Three triangles are marked out of a bigger triangle at the three vertices such that each side of each of the smaller triangles is one-fourth as long as each corresponding side of the bigger triangle. The ratio of the area of the three small triangles taken together to that of the rest of the bigger triangle is