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Sheet # 72 Critical Thinking

Name: _____________________ Date_____________

Show and explain your work. Draw pictures or make tables to explain your answer.

Each smaller square is made by joining the midpoints of the sides of the larger surrounding square. What fraction of the area of the square ABCD is the MNOP square? The area of the square ABCD is 100 sq. cm. Explain your thinking at each step and your answer(s)

Answer for sheet # 72

Since the area of the square ABCD is 100 sq. cm, side is 10 cm.

Area of Square EFGH is half the area of the square ABCD.

AE = 5 cm
AF = 5cm
Area of the triangle AEF = (5 x 5)/2 = 12.5 sq. cm
Four congruent triangles; AFE, FBG, GCH and EDH

Area of square EFGH = 100 sq cm - 50 sq. cm = 50 sq. cm

Half of the big square

Area if IJKL square is half the square EFGH.

Area of square MNOP is half the square IJKL.

Square MNOP is 1/8 of the square ABCD,