Question

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

Answer 1

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 $BO\perp AC$

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) $x=4$

∴ AO (Leg2) $=x=4$

∴ AB (hypotenuse) $=x\sqrt2=4\sqrt2=5.66$  

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) $=x=4$

CO (side opposite 60° angle) $=x\sqrt3=4\sqrt3=6.93$

BC (Hypotenuse) $=2x=2\times 4 =8$

Length of side AC is given as sum of AO and CO

$AC=AO+CO=4+6.93=10.93$

Perimeter of Δ ABC= Sum of sides of triangle

⇒ AB+BC+AC

⇒ $5.66+8+10.93$

⇒ $24.59$ units

Area of Δ ABC = $\frac{1}{2}\times base\times height$

⇒  $\frac{1}{2}\times 10.93\times 4$

⇒ $21.86$ units square