Find the area and perimeter of abc at right. give approximate (decimal) answers, not exact answers

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 'D'

Given

For Δ ABD

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:

Leg1

Leg2

Hypotenuse

where is any positive number

We are given BD(Leg 1)=4

∴ AD(Leg2)=4

∴ AB (hypotenuse)  

For Δ CBD

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:

Leg1(side opposite 30° angle)

Leg2(side opposite 60° angle)

Hypotenuse

where is any positive number

We are given BD(Leg 1)=4

∴ CD(Leg2)

∴ BC (hypotenuse)  

Length of side AC is given as sum of segments AD and CD

Perimeter of Δ ABC= Sum of sides of triangle

⇒ AB+BC+AC

⇒

⇒ units

Area of Δ ABC =

⇒  

⇒ units square