Answer:
Area of Δ ABC = 21.86 units square
Perimeter of Δ ABC = 24.59 units
Step-by-step explanation:
Given:
In Δ ABC
∠A=45°
∠C=30°
Height of triangle = 4 units.
To find area and perimeter of triangle we need to find the sides of the triangle.
Naming the end point of altitude as 'O'
Given
For Δ ABO
Since its a right triangle with one angle 45°, it means it is a special 45-45-90 triangle.
The sides of 45-45-90 triangle is given as:
We are given BO (Leg 1)
∴ AO (Leg2)
∴ AB (hypotenuse)
For Δ CBO
Since its a right triangle with one angle 30°, it means it is a special 30-60-90 triangle.
The sides of 30-60-90 triangle is given as:
We are given BO (side opposite 30° angle)
CO (side opposite 60° angle)
BC (Hypotenuse)
Length of side AC is given as sum of AO and CO
Perimeter of Δ ABC= Sum of sides of triangle
⇒ AB+BC+AC
⇒
⇒ units
Area of Δ ABC =
⇒
⇒ units square
