Enhanced Curriculum Support
This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:
Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.
Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.
Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.
Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.
Sec A
1. The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 150 m. Find the area of the triangle.
2. The length of the sides of a triangle are 5 cm, 7 cm and 8 cm. Area of the triangle is :
(a)
(b)
3. Assertion (A): The height of the triangle is 18 cm and its area is 72
Reason (R): Area of a triangle =
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true
4. Assertion (A): The sides of a triangle are 3 cm, 4 cm and 5 cm. Its area is 6
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area =
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true
5. If the area of an isosceles right triangle is 8 cm2, what is the perimeter of the triangle?
(a)
(c)
6. The perimeter of an equilateral triangle is 60 m. The area is:
(a)
(c)
Sec B
1. Find the area of equilateral triangle whose side is 12 cm using Heron's formula.
2. The base of an isosceles triangle measures 24 cm and its area is 192 cm2. Find its perimeter.
3. The length of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
4. Two sides of a triangular field are 85 m and 154 m in length and its perimeter is 324 m. Find the area of the field.
Sec C
1. Explain the significance of the semi-perimeter in Heron's formula.
2. The cost of leveling the ground in the form of a triangle having the sides 51m, 37m and 20m at the rate of Rs.3 per
OR
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its area.
3. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
OR
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs2000 per
Sec D
1. The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular field.
OR
The perimeter of a right triangle is 24 cm. If its hypotenuse is 10 cm, find the other two sides. Find its area by using the formula area of a right triangle. Verify your result by using Heron's formula.
2. Find the percentage increase in the area of a triangle if its each side is doubled. (5) OR The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 150 m. Find the area of the triangle.
3. The length of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
Problem 1
Question:A group of students decides to clean a triangular park with sides measuring 13 meters, 14 meters, and 15 meters as part of a community service project. Use Heron's Formula to find the area of the park and explain how this activity helps in developing social responsibility and teamwork.
Problem 2
Question:During a school event, the playground is divided into triangular sections with sides measuring 20 meters, 21 meters, and 29 meters. Calculate the area using Heron’s Formula. How does participation in such events promote a sense of fairness and cooperation among students?
Q1
A triangular plot of land has sides measuring 18 meters, 24 meters, and 30 meters. The owner wants to divide the plot into smaller triangular sections with equal areas for different purposes. How would you calculate the area of each smaller triangle using Heron’s Formula, and what would be the total area of the original plot? Justify why Heron’s Formula is useful for such real-life applications.
Q2
A triangular park has sides of 7 meters, 24 meters, and 25 meters. If a diagonal pathway divides the park into two smaller triangles, explain how you can use Heron’s Formula to find the areas of both triangles. Discuss the significance of dividing complex shapes into simpler triangles for area calculation in engineering and construction.
Q3
Two triangular fields have sides measuring 9 meters, 12 meters, and 15 meters for the first triangle and 8 meters, 15 meters, and 17 meters for the second. Compare the areas of these triangles using Heron’s Formula and analyze how different side lengths impact the area of a triangle even if the perimeter is nearly the same.
Q4
A triangular garden has sides of 13 meters, 14 meters, and 15 meters. After calculating the area using Heron’s Formula, the gardener plans to lay grass on 75% of the total area. How would you calculate the area that will be covered with grass? Explain the importance of applying mathematical formulas in landscaping and gardening.
Questions
1. An isosceles right triangle has area 8
(A)
(B)
(C)
(D)
2. The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is
(A)1322
(B)1311
(C)1344
(D)1392
3. The area of an equilateral triangle with side 2
(A)5.196
(B)0.866
(C)3.496
(D)1.732
4. The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude.
(A)16
(B)10
(C)24
(D)28 cm
5. The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at the rate of 9 paise per
(A)RS 2.00
(B)RS 2.16
(C)RS 2.48
(D)RS 3.00
6. The area of a triangle with base 4 cm and height 6 cm is 24
7. The area of ∆ ABC is 8
8. The base and the corresponding altitude of a parallelogram are 10 cm and 3.5 cm, respectively. The area of the parallelogram is 30
9. In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.
10. Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per
11. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per
12. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle?
13. A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.
14. A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1
15. The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
Q1
Situation: A farmer has a triangular plot of land with sides measuring 40 meters, 50 meters, and 60 meters. He plans to divide the land into smaller sections for different crops but first needs to know the total area of the plot.
Questions:
1. Using Heron’s Formula, calculate the total area of the triangular plot.
2. If the farmer wants to dedicate 60% of the plot to growing wheat, how much area will be used for wheat cultivation? Show your calculations.
Sol 1
1. The total area of the triangular plot is approximately 992.15
2. The farmer will use approximately 595.29
Q2
Scenario:A school wants to design a triangular garden with sides 26 meters, 28 meters, and 30 meters. The school management plans to install a small fountain at the center and pave a walkway around it, leaving the remaining area for grass.
Questions:
1. Use Heron’s Formula to find the total area of the triangular garden.
2. If the walkway takes up 20% of the total area, how much area will be available for planting grass?
Sol 2
1. The total area of the triangular garden is 336
2. 268.8