Open Middle®
Directions: Using the digits 0 – 9, at most one time each, fill in the blanks to make a true statement. (Note: Image is not to scale)
Hint
Which shapes two shapes can this house be decomposed into?
Which formulas can be helpful in determining areas of these shapes?
Which formulas can be helpful in determining areas of these shapes?
Answer
Answer 1: The base of the rectangle is 8, and the height is 7. The area is 56. The height of the triangle is 3. The area is 12.
Answer 2: The base of the rectange is 8, and the height is 9. The area is 72. The height of the triangle is 4. The area is 16.
Answer 3: The base of the rectangle is 8, and the height is 7. The area is 56. The height of the triangle of 1. The area is 04.
Answer 2: The base of the rectange is 8, and the height is 9. The area is 72. The height of the triangle is 4. The area is 16.
Answer 3: The base of the rectangle is 8, and the height is 7. The area is 56. The height of the triangle of 1. The area is 04.
Source: Owen Kaplinsky
12 triangle 13 square, total 156, area 78
12 triangle 13 square total 156 area 78
Rectangle – 9 by 4 Area = 36
Triangle – 4 by 5 Area = 10
Rectangle – 5 by 4 Area = 20
Triangle – 9 by 4 Area = 18
Rectangle – 7 by 6 Area = 42
Triangle – 3 by 6 Area = 09
Rectangle – 9 by 6 Area = 54
Triangle – 6 by 7 Area = 21
the areas are 16 12 and 04
Rectangle – 3 by 6 (Area = 18)
Triangle – 6 by 9 (Area = 27)
There are 17 solutions without leading zeros:
rectangle: b = 4, h = 7, A = 28
triangle: h = 5, A = 10
rectangle: b = 4, h = 8, A = 32
triangle: h = 5, A = 10
rectangle: b = 4, h = 9, A = 36
triangle: h = 5, A = 10
rectangle: b = 6, h = 5, A = 30
triangle: h = 4, A = 12
rectangle: b = 8, h = 5, A = 40
triangle: h = 3, A = 12
rectangle: b = 8, h = 7, A = 56
triangle: h = 3, A = 12
rectangle: b = 4, h = 5, A = 20
triangle: h = 8, A = 16
rectangle: b = 8, h = 9, A = 72
triangle: h = 4, A = 16
rectangle: b = 9, h = 3, A = 27
triangle: h = 4, A = 18
rectangle: b = 4, h = 5, A = 20
triangle: h = 9, A = 18
rectangle: b = 9, h = 7, A = 63
triangle: h = 4, A = 18
rectangle: b = 6, h = 5, A = 30
triangle: h = 7, A = 21
rectangle: b = 6, h = 9, A = 54
triangle: h = 7, A = 21
rectangle: b = 6, h = 5, A = 30
triangle: h = 8, A = 24
rectangle: b = 6, h = 3, A = 18
triangle: h = 9, A = 27
rectangle: b = 6, h = 5, A = 30
triangle: h = 9, A = 27
rectangle: b = 8, h = 5, A = 40
triangle: h = 9, A = 36
And 12 additional solutions with leading zeros:
rectangle: b = 4, h = 9, A = 36
triangle: h = 1, A = 02
rectangle: b = 6, h = 7, A = 42
triangle: h = 1, A = 03
rectangle: b = 6, h = 9, A = 54
triangle: h = 1, A = 03
rectangle: b = 8, h = 7, A = 56
triangle: h = 1, A = 04
rectangle: b = 8, h = 9, A = 72
triangle: h = 1, A = 04
rectangle: b = 3, h = 7, A = 21
triangle: h = 4, A = 06
rectangle: b = 4, h = 7, A = 28
triangle: h = 3, A = 06
rectangle: b = 3, h = 9, A = 27
triangle: h = 4, A = 06
rectangle: b = 3, h = 4, A = 12
triangle: h = 6, A = 09
rectangle: b = 3, h = 7, A = 21
triangle: h = 6, A = 09
rectangle: b = 6, h = 7, A = 42
triangle: h = 3, A = 09
rectangle: b = 3, h = 8, A = 24
triangle: h = 6, A = 09
The base of the rectangle is 6, and the height is 9. The area is 54. The height of the triangle is 7. The area is 21.
The base of the rectangle is 4, and the height is 5. The area is 20. The height of the triangle is 9. The area is 13.