Question

Side of eqilateral triangle PQR is 8 cm then find the area of triangle whose side is
half of side of triangle PQ​R

Answer 1

Step-by-step explanation:

triangle PQR is an equilateral triangle

PQ=QR=PR=8 m

let the triangle ABC be the triangle having sides half of triangle PQR

In triangle ABC ,

BC=AC=AB=1/2 × 8

BC = AC= AB = 4cm

triangle ABC ~ triangle PQR

because all the sides if triangle is in same proportion

AB/PQ =BC/PQ=AC/PR = 4/8 =1/2

A(triangle PQR )/A( triangle ABC ) = PQ^2/AB^2 --------( theorem of ratios of areas of similar triangles)

A( PQR ) /A (ABC) =8^2/4^2 =64/16=4/1

A( ABC)= A( PQR)/4 ------(1)

area of equilateral triangle = root3/4 ×( side)^2

A ( PQR) = root 3 /4 ×8^2 = 16 root 3 -----(2)

substituting (2) in (1)

A ( ABC) = 16 root3/4

A( ABC)= 4root3 cm

Answer 2

Given : Side of equilateral triangle PQR is 8 cm

To  find : the area of triangle whose side is half of side of triangle PQR​

Solution:

Area of equilateral triangle  =  √3 (Side)²  / 4

Area of equilateral triangle    PQR with side 8 cm

= √3 (8)²  / 4

= 16 √3 cm²

area of triangle whose side is half of side of triangle PQR​

=> Area = √3 (8/2)²  / 4

√3 (4)²  / 4

=4 √3 cm²

= (1/4) Area of equilateral trianglePQR

area of triangle whose side is half of side of triangle PQR is (1/4) Area of equilateral triangle PQR

= 4 √3 cm²

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