A quilt contains cuts of congruent right triangular pieces with a base of 8 1/2 centimeters and a height of 8 1/2 centimeters. How many triangular pieces are needed to make a rectangular quilt with an area of 4335 square centimeters?

The number of triangular pieces needed for he making of the rectangular quit is determined by dividing the area of the rectangle by the area of the pieces.

For triangular figures, the area is calculated through the equation,

A = 0.5bh

where b and h are base and height, respectively. Substituting,

A = 0.5 (8.5 cm) (8.5 cm) = 36.125 cm²

Dividing the area of the rectangle by the area of the triangle,

n = (4335 cm²) / (36.125 cm²) = 120

Therefore, 120 triangular pieces are needed for the construction of the rectangular quilt.