Math 1 · Unit 11 · Lesson 3 · part 4 of 5
The box method
When a shape has no easy base and height, use the box method .
The box method
When a shape has no easy base and height, use the box method. Draw the smallest rectangle around the shape along the grid lines. Its area is a count. Then subtract the right triangles in the corners, each one half of a leg times a leg.
Triangle (1, 1), (7, 3), (3, 6). The box runs from x = 1 to 7 and y = 1 to 6: 6 by 5, area 30. The three corner triangles have legs 6 and 2 (area 6), 4 and 3 (area 6), and 2 and 5 (area 5). Area of the triangle: 30 − 6 − 6 − 5 = 13.
Challenge: the pentagon's areaBox the pentagon C(−1, 1), D(3, 4), E(6, 0), F(2, −3), G(−4, −4) from x = −4 to 6 and y = −4 to 4: a 10 by 8 box with area 80. Then subtract the pieces outside the pentagon but inside the box. Some pieces are right triangles and one is a four-sided piece you can split into a triangle and a rectangle. The pentagon's area comes out to 38.5 square units. Try it, and check that your pieces add up to 41.5.