4×12－½×4×3 = 42cm² (Ans)

Ans : 48cm2. Number of mini triangles able to fit inside shaded area = 12cm/3cm x2 =8. Area of 1 mini triangle = 1/2 x 3cm x 4cm = 6cm2 . Total area of shaded area = 6cm2 x 8 =48cm2 .
Proof: Using similar triangles, ratio of height of small triangle (shaded one with height of 3cm) to height of large triangle (12cm). We can see that the ratio is 1:4 . Hence, the length of the base of the big triangle is 4 x base of small triangle = 4 x 4=16. Area of large triangle = 1/2 x 12 x 16 = 96cm2. Area of small the middle sized triangle ( height is 12cm-3cm=9cm) = 1/2 x 9 x (16-4) = 48cm2. Hence the area of shaded part is = 96cm2 -48cm2 = 48cm2

48=4×12

It is the rectangle area. Not the shaded part