Question

PQRS is a rhombus. find the ratio of area of rhombus PQRS to the area of triangle PQR​

Answer 1

the ratio will be 2:1

Answer 2

Answer:

The ratio of Ar (Rhombus) : Ar (Triangle) = 2 : 1

Step-by-step explanation:

Let’s get into the basics when solving this problem:-

Rhombus – It can best be described as a four sided figure. So it is a quadrilateral but does not have a right angle formed at the vertex. It can also be best described as a square that is slanted (not having any right angles). When calculating the area of a  Rhombus you can use the formulae:-

Area of a rhombus PQRS = Base X Height.

Triangle – It is a three sided figure that can have three vertex and three angles. But in general if we speak of calculating the area of a triangle we can use the formulae:-

Area of a triangle PQR = Base X Height.

Now calculating the ratio of two:-

Area of Rhombus PQRS : Area of Triangle PQR

Keeping QS and RP as Diagonals of Rhombus and QS as common height of the Triangles formed by the Rhombus….. we get

Area of Rhombus = Base X Height

 = RP X QT ( ‘ T’ is the midpoint of QS)

Area of triangle = ½ Base X Height

 = ½ RP X QT ( QT is perpendicular to base RP)

Ratio = RP X QT = ½ RP X QT

Cancelling RP X QT we get…… Area of Rhombus : Area of Triangle = 1 : ½

Area of Rhombus : Area of Triangle =  2 : 1