Question

Find area of quadrilateral ABCD in which AB =3cm, diagonal AC=4cm,AB is Perpendicular to AC and ADC is equilateral. Also find perimeter

Answer 1

check it out above for step by step explanation.

perimeter = sum of all the sides

= 4cm+4cm+5cm+3cm

= 16cm

Answer 2

Area of quadrilateral ABCD=$(6+4\sqrt 3) cm^2$

Perimeter of quadrilateral ABCD=24 cm

Step-by-step explanation:

AB=3 cm

AC= 4cm

AB is perpendicular to AC

Therefore, triangle ABC is a right triangle.

Area of triangle=$\frac{1}{2}\times Base\times height$

Using the formula

Area of triangle ABC=$\frac{1}{2}\times AC\times AB=\frac{1}{2}\times 4\times 3=6 cm^2$

ADC is an equilateral triangle

All sides of equilateral triangle are equal.

Side of equilateral triangle =AC=4 cm

Area of equilateral triangle =$\frac{\sqrt 3}{4}(side)^2$

Using the formula

Area of equilateral triangle ADC=$\frac{\sqrt 3}{4}(4)^2=4\sqrt 3cm^2$

Area of quadrilateral ABCD=Area of triangle ABC+area of triangle ADC

Area of quadrilateral ABCD=$(6+4\sqrt 3) cm^2$

In triangle ABC

$BC^2=AC^2+AB^2$

Using Pythagoras theorem  

$(hypotenuse)^2=(Base)^2+(perpendicular\;side)^2$

$BC^2=3^2+4^2=9+16=25$

$BC=\sqrt{25}=5 cm$

Perimeter of triangle ABC=AB+BC+AC=3+4+5=12 cm

Perimeter of triangle ADC=$3(side)=3(4)=12 cm$

Perimeter of quadrilateral ABCD=Perimeter of triangle ABC+perimeter of triangle ADC=12+12=24 cm

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