Name: Area of a Quadrilateral and Rhombus
Uploaded: 2019-07-19
Duration: 8 min 51 s

Question

Find the area of the quadrilateral $A B C D$ in which $B C D$ is an equilateral triangle, each of whose sides is $26 cm, A D = 24 cm$ and $∠ B A D = 90 °$ . Also, find the perimeter of the quadrilateral. (Given, $\sqrt{3} = 1.73$ ).

Accepted Answer

In $∆ A B D$

Using the Pythagoras theorem, we get:

$B D^{2} = A B^{2} + A D^{2}$

By substituting the values,

$26^{2} = A B^{2} + 24^{2}$

$A B^{2} = 676 - 576$

$A B^{2} = 100$

$A B = \sqrt{100}$

Thus, Base $= A B = 10 cm$

We know that area of $∆ A B D = \frac{1}{2} \times b a s e \times h e i g h t$

By substituting the values,

Area of $∆ A B D = \frac{1}{2} \times 10 \times 24$

On further calculation,

Area of $∆ A B D = 120 {cm}^{2}$

We know that the area of $∆ B C D = \frac{\sqrt{3}}{4} a^{2}$ ( $∵$ It is an equilateral triangle)

By substituting the values,

Area of $∆ B C D = (\frac{1.73}{4}) (26)^{2}$

Area of $∆ B C D = 292.37 {cm}^{2}$

So we get the area of quadrilateral $A B C D =$ Area of $∆ A B D +$ Area of $∆ B C D$

By substituting the values,

Area of quadrilateral $A B C D = 120 + 292.37$

Area of quadrilateral $A B C D = 412.37 {cm}^{2}$

The perimeter of quadrilateral $A B C D = A B + B C + C D + D A$

By substituting the values,

Perimeter $= 10 + 26 + 26 + 24$

So we get,

Perimeter $= 86 cm$

Therefore, the area is $412.37 {cm}^{2}$ and perimeter is $86 cm$ .

Find the area of the quadrilateral $A B C D$ in which $B C D$ is an equilateral triangle, each of whose sides is $26 cm, A D = 24 cm$ and $∠ B A D = 90 °$ . Also, find the perimeter of the quadrilateral. (Given, $\sqrt{3} = 1.73$ ).

Important Questions on Areas of Triangles and Quadrilaterals

Learn and Prepare for any exam you want !

Find the area of the quadrilateral ABCD in which BCD is an equilateral triangle, each of whose sides is 26 cm, AD=24 cm and ∠BAD=90°. Also, find the perimeter of the quadrilateral. (Given, 3=1.73).

Important Questions on Areas of Triangles and Quadrilaterals

Learn and Prepare for any exam you want !

Find the area of the quadrilateral $A B C D$ in which $B C D$ is an equilateral triangle, each of whose sides is $26 cm, A D = 24 cm$ and $∠ B A D = 90 °$ . Also, find the perimeter of the quadrilateral. (Given, $\sqrt{3} = 1.73$ ).