 Hello friends, let's discuss the following question. It says find the area of a quadrilateral abcd in which ab is 3 cm, bc is 4 cm, cd is 4 cm, dA is 5 cm and ac is 5 cm. So we have to find the area of quadrilateral having these dimensions. For that we will be using here Ron's formula to find the area of triangle which says that if we have a triangle say abc having size say abc then s is given by a plus b plus c by 2 and the area of triangle abc is given by under the root of s into s minus a s minus b into s minus c cm square. So this knowledge will work as key idea for the question. To find the area of the quadrilateral we will first find the area of triangle abc and then we will find the area of triangle acd and then we will add the two areas to get the area of quadrilateral abcd. Now in triangle abc ab is 3 cm, bc is 4 cm, cd is 5 cm. To obtain the area of the triangle we will be using here Ron's formula for that we need to find s which is given by 3 plus 4 plus 5 upon 2 which is equal to 6. Now we will find the area of triangle abc by this formula where s is 6 into 6 minus 3 into 6 minus 4 into 6 minus 5. This is equal to under the root of 6 into 3 into 2 into 1. This is equal to 6 cm square. Now we have to find the area of triangle acd. So in triangle acd ac is 5 cm, cd is 4 cm, ad is 5 cm. Now we find s which is 5 plus 4 plus 5 upon 2 which is equal to 7. Now we find area of triangle acd by Ron's formula which is s into s minus a into s minus b into s minus c is equal to under the root of 7 into 2 into 3 into 2. This is equal to 9.2 cm square approximately. Now area of quadrilateral is equal to area of triangle abc plus area of triangle acd. Now area of triangle abc is 6 cm square and area of triangle acd is 9.2 cm square approximately. So the total area is 15.2 cm square approximately. Hence the area of quadrilateral is 15.2 cm square approximately. So this completes the question. Bye for now. Take care. Have a good day.