Tuesday

Rocket holds up a paper triangle. "The porch roof. I need its area, and triangles have no rows of squares."

Raven cuts an identical triangle and turns it upside down. She slides it against the first one.

"What do you notice?" she asks.

"A parallelogram," Rocket says. "Two triangles make a parallelogram. So one triangle is half."

"Half of base times height," Raven says, writing it down. "½ × 8 × 5."

Nova drifts over the two shapes. "And the porch floor?" she asks. "The one with two parallel sides?"

Rocket looks at the trapezoid for a long moment. Then he grabs the scissors and cuts it corner to corner.

"Two triangles," he says. "Same height, different bases." Nova hums. "Now you are cutting like a designer."

Two copies of any triangle fit together to make a parallelogram with the same base and the same height.

So a triangle has half the area: ½ × base × height. This triangle is ½ × 8 × 5 = 20 square centimeters.

The height is measured straight from the base to the top corner. For a right triangle, one leg is the height.

A trapezoid has two parallel sides, a top and a bottom. Cut it corner to corner and you get two triangles.

Both triangles have height 3. One has base 4, the other base 8. Add their areas: ½ × 4 × 3 + ½ × 8 × 3.

That is the same as ½ × (4 + 8) × 3 = 18 square centimeters. Add the parallel sides, halve, multiply by the height.

Half, and two halves. Tomorrow is Build Lab: cut real grid-paper shapes and count the squares yourself.