The area of a triangle is half the product of its base and height: A=21bh.
Every triangle is exactly half of a rectangle with the same base and height — cut the rectangle along the diagonal.
Showing a random 20 of 50 problems.
Example 1
hard
A triangle's vertices are (1,1), (6,1), (4,8). Find its area.
Example 2
medium
Find the area of an equilateral triangle with side 6 (use 3≈1.73).side = 6 for all three; find area (use √3 ≈ 1.73)
Example 3
easy
Find the area of a triangle with base 10 and height 6.base = 10, height = 6
Example 4
easy
A right triangle has legs 9 and 40. Find its area.
Example 5
medium
A triangle has sides 7 and 10 with included angle 30°. Find its area.
Example 6
easy
What units does triangle area have if base and height are in m?
Example 7
medium
A triangular flag has base 24 in and height 18 in. How many square feet of fabric does it need?
Example 8
hard
A triangle has base b on the x-axis and a vertex at (x0,y0) with y0>0. Explain why its area equals 21b⋅y0.
Example 9
easy
Why must we divide by 2 in the triangle area formula?
Example 10
easy
A triangle has area 24 and base 8. Find its height.base = 8, area = 24; find height h = ?
Example 11
challenge
A triangle has sides 3, 4, 5 inscribed with a smaller similar triangle whose sides are half. Compare areas.
Example 12
hard
In a triangle, the three medians all split it into two equal-area triangles. True or false?
Example 13
hard
A triangle has vertices (0,0), (6,0), (0,8). Find the inradius given area 24 and perimeter 24 (sides 6, 8, 10).
Example 14
medium
A triangle's base is tripled and its height is unchanged. How does its area change?
Example 15
medium
A triangular garden has base 12 m and height 9 m. Bags of soil cover 6 m² each. How many bags are needed?base = 12 m, height = 9 m; area = ½ × 12 × 9
Example 16
medium
Two triangles share the same base and have the same height. How do their areas compare?
Example 17
medium
A triangle has an obtuse angle, with base 10 and the perpendicular height (which falls outside the triangle) measuring 4. Find the area.base = 10, perpendicular height = 4 (falls outside triangle)
Example 18
easy
Find the area of a triangle with base 20 and height 3.
Example 19
easy
A right triangle has legs 5 and 12. Find its area.
Example 20
easy
A triangle has area 30 and height 5. Find its base.height = 5, area = 30; find base b = ?