Question

A sign manufacturer makes yield signs by cutting an equilateral triangle from a square piece of aluminum with the dimensions shown. The height of the yield sign to the nearest tenth is __31.2___ inches. (Enter only the number.)

QUESTION #1.The area of the yield sign to the nearest tenth of a square inch is ______ in2.

QUESTION #2.How much material is left after the yield sign is made? A.734.8 in2 B.1028 in2 C.829.6 in2 D.1296 in2

Answer 1

Let h be the height & 2x be the length of the equilateral triangle.
h^2=(2x)^2-x^2
h^2=4x^2-x^2=3x^2
x=h/sqrt3=31.2/1.732=18.0 to tenth place
2x=2*18=36
side of square piece =36
area of a square=36*36=1296 sq. inches
Area of triangle=1/2(2x)h=1/2(36)*31.2=561.6 inches
remaining area=1296-561.6=734.4 inches