Triangle Area — Half a Rectangle - AskRobots.com

Animation coming — full Sora 2 prompt below. Video will replace this placeholder.

Plain English first

Draw a rectangle. Now cut it diagonally from corner to corner. You get two identical triangles. Each triangle is exactly half the rectangle.

That's the whole formula. A triangle with the same base and height as a rectangle always contains exactly half the area. The ½ in A = ½bh is not a magic number — it's literally the diagonal cut.

This means to find a triangle's area, you don't need to count unit squares directly. Find what rectangle would surround it, compute that area, then take half.

Standard math notation

A = ½ × b × h

Where:
  A = area of the triangle
  b = base (the bottom edge length)
  h = height (perpendicular distance from base to opposite vertex)

Note: h must be perpendicular to b — not the slant side length.
      For a right triangle, h is one of the legs.

Verbose Python with descriptive names

def compute_triangle_area(
    length_of_base,
    perpendicular_height_from_base_to_apex
):
    """
    A triangle is exactly half of the rectangle that surrounds it.
    Draw the rectangle: base × height gives the full rectangle area.
    The diagonal cut gives us half of that.
    """
    area_of_surrounding_rectangle = length_of_base * perpendicular_height_from_base_to_apex
    area_of_triangle = area_of_surrounding_rectangle / 2
    return area_of_triangle

area = compute_triangle_area(
    length_of_base=6,
    perpendicular_height_from_base_to_apex=4
)
print(f"Area: {area} square units")  # 12.0

# Works for any triangle — right, acute, obtuse
# As long as h is the perpendicular height, not a slant side
area_obtuse = compute_triangle_area(
    length_of_base=8,
    perpendicular_height_from_base_to_apex=3
)
print(f"Area: {area_obtuse} square units")  # 12.0

Sora 2 video prompt

8-second animation. A blue rectangle appears labeled base b and height h,
filled with a grid. A diagonal line slices it corner to corner. One triangle
glows orange, the other fades to 30% opacity. The formula A = ½ × b × h builds
onscreen — the ½ highlights as the orange half of the rectangle. Numbers:
b=6, h=4, A=12. Clean white background, warm earth tones, satisfying diagonal
cut motion.

The perpendicular height trap

The most common mistake: using a slant side as h.

# RIGHT TRIANGLE — easy, the legs are perpendicular
area = compute_triangle_area(
    length_of_base=3,
    perpendicular_height_from_base_to_apex=4  # the vertical leg IS the height
)
# = 6

# OBTUSE TRIANGLE — height drops outside the base
# You may need to extend the base line to drop a perpendicular from the apex
# The formula still works, as long as h is truly perpendicular to b

Builds on

Rectangle Area — Counting the Grid

結果

Triangle Area — Half a Rectangle