###### Advertisements

###### Advertisements

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?

###### Advertisements

#### Solution

For each triangular piece,

Semi-perimeter,

`s=(20+50+50)/2=60 cm`

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of each triangle piece "=[sqrt(60(60-50)(60-50)(60-20))]cm^2`

`=[sqrt(60(10)(10)(40))]cm^2`

`=200sqrt6cm^2`

Since there are 5 triangular pieces made of two different coloured cloths,

`"Area of each cloth required "=(5xx200sqrt6)cm^2=1000sqrt6cm^2`

#### APPEARS IN

#### RELATED QUESTIONS

A triangle and a parallelogram have the same base and the same area. If the sides of triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

Find the area of a quadrilateral ABCD is which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Area of PQRS = Area of PQR + Area of ΔPQS = (6+9.166)𝑐𝑚2=15.166𝑐𝑚2

The perimeter of a triangullar field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.

Find the area of an equilateral triangle having altitude *h* cm.

The base of an isosceles right triangle is 30 cm. Its area is

The sides of a triangle are 50 cm, 78 cm and 112 cm. The smallest altitude is

The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is

In the given figure, the ratio *AD* to *DC* is 3 to 2. If the area of Δ ABC is 40 cm^{2}, what is the area of Δ* BDC*?

Find the area of a quadrilateral ABCD whose sides are AB = 13 cm, BC = 12 cm, CD = 9 cm, AD = 14 cm and diagonal BD = 15 cm

A park is in the shape of a quadrilateral. The sides of the park are 15 m, 20 m, 26 m and 17 m and the angle between the first two sides is a right angle. Find the area of the park

A land is in the shape of rhombus. The perimeter of the land is 160 m and one of the diagonal is 48 m. Find the area of the land.

The adjacent sides of a parallelogram measures 34 m, 20 m and the measure of the diagonal is 42 m. Find the area of parallelogram

The area of the equilateral triangle is `20sqrt(3)` cm^{2} whose each side is 8 cm.