Step-by-step explanation:
the area of a rectangle is length×width.
area of the original rectangle (before its sides are. multiplied) :
Ao = length original × width original
length new = length original × 4
width new = width original × 4
the area of the new rectangle is then :
An = length new × width new =
= length original × 4 × width original × 4 =
= length original × width original × 4 × 4 =
= length original × width original × 16 =
= Ao × 16
so, the fourth answer option is correct. the area increases by a factor 16.
two objects of shapes are similar, if their angles are the same, and exchanged side length of one object correlates with the corresponding side length of the other b object with the same ratio.
we see the ratio of one corresponding pair of side lengths is 2/4 = 1/2. so, every side length of the small prism is half as long as the corresponding side length in the large prism.
the volume of such a prism is the multiplication of 3 side lengths : length, width, height.
each one has now a scaling factor of 1/2.
so, the volume decreases by the cube of the scaling factor: 1/2×1/2×1/2 = 1/2³ = 1/8
so,
Vsmall = Vlarge × 1/8 = 2720/8 = 340 cm³
therefore, again, the fourth answer option is correct.
