chapter-header

NCERT Solutions Class 9 Mathematics Solutions for Heron’s Formula - Exercise 12.2 in Chapter 12 - Heron’s Formula

Question 2 Heron’s Formula - Exercise 12.2

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm

and AC = 5 cm.

Answer:

First, construct a diagram with the given parameter

NCERT Mathematics Solutions - Class 9 chapter Heron’s Formula Question 2 Solution image

Now, apply the Pythagorean theorem in ΔABC

NCERT Mathematics Solutions - Class 9 chapter Heron’s Formula Question 2 Solution image

Video transcript
"hello students welcome to lito q a video session i am saf your maths tutor and question for today is find the area of quadrilateral abcd in which a b is equal to 3 centimeter bc is equal to 4 centimeter cd is equal to 4 centimeter da is equal to 5 centimeter and ac is equal to 5 centimeter so here if you consider quadrature abcd it is a combination of two triangles triangle abc and triangle adc to find the sum quad the total area of this quadrilateral you do some triangle abc and triangle adc's area so first of all let us find the area of the triangle abc so area of triangle abc that is the heading to find area of triangle abc we need to find semi perimeter first so semi perimeter is equal to 3 plus 4 plus 5 upon 2 which is s is equal to 3 plus 4 plus 5 12 upon 2 and that is 6 6 centimeter now you know formula of area that is haron's formula so as per heron's formula area can be given by root of s s minus a s minus b and s minus c this is the formula to find area of the given triangle so root of s is 6 6 6 minus three six minus four six minus five root off six into three into two into one that is 6 into 6 and that is 6 square and hence finally you will get root of that will be 6 centimeter square that is our area of triangle abc this a is now we have found the area of triangle abc now let us look for triangle adc to find the area of triangle adc we have to use the same method so i'll rub it over here and continue here i'll give heading area of triangle adc to find area of triangle adc we know the harrow's formula to find area that is area of triangle is equal to root of s s minus a s minus b s minus c so as per haran's formula where s is the semi perimeter and abc are the sides of the triangle here a is equal to phi b is equal to 4 and c is equal to 5 so s can be given as a plus b plus c upon 2 and that is 5 plus 4 plus 5 upon 2 so s value comes out to be 7 meter or it is 7 centimeter so 7 centimeter is our semi perimeter now you can find the area by using heron's formula to find area using harold's formula let us do it over here remember s is equal to 7 centimeter so area of the triangle can be given by root of 7 7 minus 5 7 minus 4 and 7 minus 5 so that is root of 7 into 2 into 3 into 2 so that comes out to be 2 under root of 21 and that is one 9.16 centimeter square so this is the area of triangle adc now we have two areas area of triangle adc as well as area of triangle abc we can sum this both area so area of quadrilateral a b c d is equal to area off we will sum them up triangle adc plus triangle abc so we have to sum their area now we will do it over here any area of quadrilateral will be equal to area of both the inner triangle and that is 6 plus 9.16 that is centimeter square and hence it is 15.16 centimeter square so this is the required value for the area or you can approximate your answer round it off as 15.2 centimeter square so that is our area of quadrilateral abcd if you have any query you can drop it in our comment section and subscribe to ledo for more such q a thank you for watching "
Connect with us on social media!
2022 © Quality Tutorials Pvt Ltd All rights reserved