Question

message "KEEP THE PARK GREEN AND CLEAN" (see Fig. 12.10 ). If the sides of the
There is a slide in a park. One of its side walls has been painted in some colour with a
15 m, 11 m and 6 m, find the area painted in colour.
203
MARMOLA
wall are
6 m
11 m
KEEP THE PARK
GREEN AND CLEAN
15 m
Fig. 12.10
inngle two sides of which are 18cm and 10cm and the perimeter is​

Answer 1

Answer:

20√2m²

Step-by-step explanation:

The perimeter of a triangle is equal to the sum of its three sides it is denoted by 2S.

2s=(a+b+c)

s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

The formula given by Heron about the area of a triangle is known as Heron's formula.

According to this formula area of a triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle and s is a semi perimeter.

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily .

Heron's formula is generally used for calculating area of scalene triangle.

___________________ _________________

Solution:

Here area painted in colour will be equal to the area of triangle with side 15m,11m and 6 m

Let the Sides of the triangular wall are a=15 m, b=11 m & c=6 m.

Semi Perimeter of the ∆,s = (a+b+c) /2

Semi perimeter of triangular wall (s) = (15 + 11 + 6)/2 m = 16 m

Using heron’s formula,

Area of the wall = √s (s-a) (s-b) (s-c)

= √16(16 – 15) (16 – 11) (16 – 6)

= √16 × 1 × 5 × 10

= √ 4×4×5×5×2

= 4×5√2

= 20√2 m²

Hence, the area painted in colour is 20√2 m².

Answer 2

S = a +b+c/2

S= 15 + 11 + 6/2

S = 32/2

S = 16

Area =

$\sqrt{s(s - a)(s - b)(s - c)} \\ \\ \\ \sqrt{16(16 - 15)(16 - 11)(16 - 6) }$4×4×5×2