Question

Find the area of a quadrilateral ABCD in which AD= 24 cm, BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm. (Take √3 = 1.73)

Answer 1

The area of a quadrilateral ABCD is $\mathbf{412.37 \ cm^{2}}$

Step-by-step explanation:

• Given data

        Here ABCD is quadrilateral.

        AD = 24 cm

• ΔBCD is an equilateral triangle, so

        BC = CD = BD = 26 cm

• ΔABD is a right angle triangle.

        ∠BAD = 90°

        AD = 24 cm

        and

        BD =26 cm     (Hypotenuse)

        So

        $\mathbf{AB =\sqrt{BD^{2}-AD^{2}}}$

        $\mathbf{AB =\sqrt{26^{2}-24^{2}} = 10 \ cm}$

• Here ΔABD is a right angle triangle where AB⊥AD

        So area of ΔABD is given below

        $\mathbf{area \ \Delta ABD =\frac{1}{2}\times AB\times AD}$

        $\mathbf{area \ \Delta ABD =\frac{1}{2}\times 10\times 24=120}$     ...1)

• Now ΔBCD is an equilateral triangle, which side is equal to 26 cm.

       From formula of area of equilateral triangle

        $\mathbf{\textrm{Area of an equilateral triangle}=\frac{\sqrt{3}}{4}\times Side^{2}}$

        $\mathbf{\textrm{Area of an equilateral triangle}=\frac{1.73}{4}\times 26^{2}}$

        $\mathbf{\textrm{Area of an equilateral triangle}=292.37}$       ...2)

• Then

        Area of quadrilateral ABCD =Area of ΔABD +Area of ΔBCD

        Area of quadrilateral ABCD = 120 + 292.37 $\mathbf{=412.37 \ cm^{2}}$

Answer 2

Answer: 412.37 m square

Step-by-step explanation:

Given data

        Here ABCD is quadrilateral.

        AD = 24 cm

ΔBCD is an equilateral triangle, so

        BC = CD = BD = 26 cm

ΔABD is a right angle triangle.

        ∠BAD = 90°

        AD = 24 cm

        and

        BD =26 cm     (Hypotenuse)

        So

       

       

Here ΔABD is a right angle triangle where AB⊥AD

        So area of ΔABD is given below

       

            ...1)

Now ΔBCD is an equilateral triangle, which side is equal to 26 cm.

       From formula of area of equilateral triangle

       

       

              ...2)

Then

        Area of quadrilateral ABCD =Area of ΔABD +Area of ΔBCD

        Area of quadrilateral ABCD = 120 + 292.37

= 412.37 m square