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# Help pls A sheet of paper \$12\$ inches by \$18\$ inches is folded so that two opposite corners touch, as shown in the figures below. What is th

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Help Pls With This question : A sheet of paper \$12\$ inches by \$18\$ inches is folded so that two opposite corners touch, as shown in the figures below. What is the area, in square inches, of the shaded triangle formed where the paper overlaps itself?[asy] size(350); defaultpen(linewidth(0.8)+fontsize(10)); picture p; pen ds = linewidth(3.5); pair D = (0,0), C = (3,0), B = (3,2), A = (0,2); draw(A--B--C--D--cycle); dot(A,ds); dot(B,ds); dot(C,ds); dot(D,ds); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); real theta = atan(5/12); pair B1 = 2*expi(theta)+A, E = (5/6,0), F = (3-5/6,2); draw(p,A--D--E--F--B1--cycle); filldraw(p,A--E--F--cycle,gray(0.6)); dot(p,A,ds); dot(p,D,ds); dot(p,B1,ds); label(p,"A,\,C",A,NW); label(p,"D",D,SW); label(p,"B",B1,(0.2,1)); add(shift(10,0)*p); [/asy]

Dec 5, 2021

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Hi there!  The area is 62 square inches.  Hope this helps!

Dec 5, 2021
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Area = 1/2(12 * 18 - 5 * 12) = 78

Dec 5, 2021