Area of Triangle for Acute, Obtuse and Right Triangles

Transcript

Area of Triangle for Acute, Obtuse and Right TrianglesAcute, Obtuse and Right Triangles are Let’s find Area of each of them using our formula For Acute Angled Triangle In ∆ABC, Height = AD = h = 3 cm Base = BC = b = 4 cm Area of ∆ABC = 1/2 × b × h = 𝟏/𝟐 × 4 × 3 = 2 × 3 = 6 cm2 ∴ Area of ∆ABC is 6 cm2 For Right Angled Triangle In Right angled triangle ∆ ABC AB ⊥ BC Thus, Height = AB = h = 3 cm Base = BC = b = 4 cm Area of ∆ABC = 1/2 × b × h = 𝟏/𝟐 × 4 × 3 = 2 × 3 = 6 cm2 ∴ Area of ∆ABC is 6 cm2 For Obtuse Triangle If we draw perpendicular from A on BC It is outside the triangle Now, we can write Area ∆ ABC as Area of ∆ ABC = Area of ∆ ADC – Area of ∆ ADB = 1/2 × DC × AD – 1/2 × DB × AD = 𝟏/𝟐 × AD × (DC – DB) Since DC – DB = BC = 𝟏/𝟐 × AD × BC So, it doesn’t matter if the height is outside the triangle, our formula remains the same Now, in ∆ ABC Height = AD = h = 4 cm Base = BC = b = 5 cm Area of ∆ABC = 1/2 × b × h = 𝟏/𝟐 × 5 × 4 = 5 × 2 = 10 cm2 ∴ Area of ∆ABC is 6 cm2