Question

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

Answer 1

Solution:

Since rhombus is the geometrical figure having   four sides equal in magnitude and having pair of parallel sides.

We know that diagonals PR and QS  divides the rhombus in two equal triangles  ΔPQR and ΔPSR

therefore

Area of Rhombus = Area of ΔPQR + Area of ΔPSR

Since:  

area of ΔPQR= area of ΔPSR

so

Area of Rhombus = area of ΔPQR + area of ΔPQR

Area of Rhombus = 2(area of ΔPQR)

Now we see area of rhombus PQRS is twice the area of triangle ΔPQR

so their ratio is

Area of Rhombus  :  area of ΔPQR = 2 : 1

Hence 2 : 1 is required ratio.

Answer 2

Answer:

area of rhombus PQRS : Area of Δ PQR  :: 2:1

Step-by-step explanation:

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

area of rhombus PQRS = Area of Δ PQR  +  Area of Δ PSR

Δ PQR  has sides  PQ , QR & PR

Δ PSR  has sides  PS , RS & PR

rhombus has all sides equal

so PQ = QR = PS = RS

& PR is common

=> Δ PQR & Δ PSR are equivalent

=> Area of Δ PQR = Area of Δ PSR = A

area of rhombus PQRS = Area of Δ PQR + Area of Δ PSR

=>area of rhombus PQRS = A + A = 2A

area of rhombus PQRS/Area of Δ PQR  = 2A/A = 2

area of rhombus PQRS : Area of Δ PQR  :: 2:1