Calculate the perimeter and area of triangles and quadrilaterals, and apply Heron's formula for triangles with known sides.
For a triangle with sides a, b, c, area=√[s(s−a)(s−b)(s−c)], where s=(a+b+c)/2 is the semi-perimeter — useful when height isn't directly known.
Find the area of a triangle with sides 9, 12, 15 cm using Heron's formula.
s=18; area=√[18×9×6×3]=√2916=54 cm²
Find the area of a triangle with sides 6, 8, 10 cm.
s=12; area=√[12×6×4×2]=√576=24 cm²
A quadrilateral's area can be found by splitting it into two triangles using a diagonal, then applying Heron's formula or the standard triangle area formula to each.
A quadrilateral field is split by a diagonal into two triangles with areas 40 m² and 55 m². Find the total area.
40+55=95 m²
Why is splitting a quadrilateral into triangles a common approach for finding its area?
Because triangle area formulas (like Heron's) are well established, and any quadrilateral can be decomposed into two triangles using a diagonal
1. Find the area of a triangle with sides 5, 12, 13 cm using Heron's formula.
2. Find the area of a triangle with sides 7, 24, 25 cm.
3. A quadrilateral field is split into triangles of area 30 m² and 45 m². Find the total area.
4. Find the perimeter of a triangle with sides 8, 15, 17 cm.
5. Find the area of an equilateral triangle with side 10 cm using Heron's formula.