Question

find the area of glass printing which ha a triangle on a square as given in the figure​

Answer 1

» Question :

Find the area of glass printing which has a triangle on it's top and a square in the bottom .

» To Find :

The Area of the figure.

» Given :

• Side of the square = 30 cm

• Total Height of the figure = 38 cm

» We Know :

Area of square :

$\sf{\underline{\boxed{A_{s} = (a)^{2}}}}$

Area of Triangle :

$\sf{\underline{\boxed{A_{t} = \dfrac{1}{2} \times b \times h}}}$

» Concept :

We Know that the the figure is divided Into two significant figures ,i.e. a square and a triangle.

So the sum of the areas of Square and triangle will give the area of the figure.

Before finding the area of the figure , let's find the sides ,which will be helpful in finding area of the square and the triangle .

As the bottom figure is a square , so all it's side will be Equal .

ATQ,

$\sf{DE = 30 cm}$

And as all it's sides are equal ,i.e. DE = BE = CB = DC ,we get the other sides as :

$\sf{\therefore DE = BE = CB = DC = 30 cm}$

In the top part ,it said that the figure is a triangle ,so the base of the triangle will be Equal to the side of square CB.

Hence ,the base of the triangle is 30 cm.

We know that the AP = 38 cm and FP = 30 cm ,so

AP - FP ,will give the length AF which is the height of the triangle.

$\sf{\Rightarrow AP - PF = AF}$

$\sf{\Rightarrow 38 - 30 = AF}$

$\sf{\Rightarrow 8 cm = AF}$

Hence ,the height of the triangle is 8 cm

Now using the found values ,we can find the area of the triangle and the square and sum them to find the area of the figure.

» Solution :

Area of the Square :

• Side = a → 30 cm

Formula =

$\sf{\underline{\boxed{A_{s} = (a)^{2}}}}$

Putting the value in the formula ,we get :

$\sf{\Rightarrow A_{s} = 30^{2}}$

$\sf{\Rightarrow A_{s} = 900 cm^{2}}$

Hence, the area of the Square is 900 cm².

Area of the triangle :

• Base = 30 cm

• Height = 8 cm

Formula :

$\sf{\underline{\boxed{A_{t} = \dfrac{1}{2} \times b \times h}}}$

Putting the value in the formula ,we get :

$\sf{\Rightarrow A_{t} = \dfrac{1}{2} \times 30 \times 8}$

$\sf{\Rightarrow A_{t} = \dfrac{1}{\cancel{2}} \times \cancel{30} \times 8}$

$\sf{\Rightarrow A_{t} = 15 \times 8}$

$\sf{\Rightarrow A_{t} = 120 cm^{2}}$

Hence ,the area of the triangle is 120 cm².

Area of the figure :

Area of the figure = Area of Square + Area of triangle

$\sf{\Rightarrow A_{f} = 900 + 120}$

$\sf{\Rightarrow A_{f} = 1020 cm^{2}}$

Hence ,the area of the figure is 1120 cm².

» Additional information :

• Total Surface Area of a Cuboid = 2(lb + lh + bh)

• Total Surface Area of a cube = 6(a)²

• Curved surface area of a Cube = 4(a)²

• Curved surface area of a Cuboid = 2(l + b)h