![\"Area](\"https:\/\/manishchandra.org\/p6\/mathAreaandPerimeterworksheet1.png\")
<\/p>\n
1. Area of 2D Shapes<\/h2>\na) Rectangle:<\/h3>\n
Area = Length \u00d7 Width<\/p>\n
Example: A rectangular garden is 10m long and 5m wide. Its area is 10m \u00d7 5m = 50 sq m.<\/p>\n<\/div>\n
b) Square:<\/h3>\n
Area = Side \u00d7 Side (Side\u00b2)<\/p>\n
Example: A square tile has a side of 30cm. Its area is 30cm \u00d7 30cm = 900 sq cm.<\/p>\n<\/div>\n
c) Triangle:<\/h3>\n
Area = (1\/2) \u00d7 Base \u00d7 Height<\/p>\n
Example: A triangle has a base of 8cm and a height of 6cm. Its area is (1\/2) \u00d7 8cm \u00d7 6cm = 24 sq cm.<\/p>\n<\/div>\n
d) Parallelogram:<\/h3>\n
Area = Base \u00d7 Height<\/p>\n
Example: A parallelogram has a base of 10cm and a height of 5cm. Its area is 10cm \u00d7 5cm = 50 sq cm.<\/p>\n<\/div>\n
e) Circle:<\/h3>\n
Area = \u03c0r\u00b2 (where \u03c0 \u2248 3.14 and r is the radius)<\/p>\n
Example: A circle has a radius of 7cm. Its area is approximately 3.14 \u00d7 7cm \u00d7 7cm = 153.86 sq cm.<\/p>\n<\/div>\n
f) Trapezium:<\/h3>\n
Area = (1\/2) \u00d7 (Sum of parallel sides) \u00d7 Height<\/p>\n
Example: A trapezium has parallel sides of 10cm and 12cm, and a height of 8cm. Its area is (1\/2) \u00d7 (10cm + 12cm) \u00d7 8cm = 88 sq cm.<\/p>\n<\/div>\n
2. Volume of 3D Shapes<\/h2>\na) Cube:<\/h3>\n
Volume = Side \u00d7 Side \u00d7 Side (Side\u00b3)<\/p>\n
Example: A cube has a side of 4cm. Its volume is 4cm \u00d7 4cm \u00d7 4cm = 64 cubic cm.<\/p>\n<\/div>\n
b) Cuboid:<\/h3>\n
Volume = Length \u00d7 Width \u00d7 Height<\/p>\n
Example: A cuboid is 5m long, 3m wide, and 2m high. Its volume is 5m \u00d7 3m \u00d7 2m = 30 cubic m.<\/p>\n<\/div>\n
c) Cylinder:<\/h3>\n
Volume = \u03c0r\u00b2h (where \u03c0 \u2248 3.14, r is the radius, and h is the height)<\/p>\n
Example: A cylinder has a radius of 7cm and a height of 10cm. Its volume is approximately 3.14 \u00d7 7cm \u00d7 7cm \u00d7 10cm = 1538.6 cubic cm.<\/p>\n<\/div>\n
Applications of Mensuration<\/h2>\n\n1. Construction:<\/h3>\n
Calculating the amount of material needed for building projects (e.g., bricks, cement, paint).<\/p>\n<\/div>\n
\n2. Packaging:<\/h3>\n
Designing boxes and containers to hold products efficiently.<\/p>\n<\/div>\n
\n3. Gardening:<\/h3>\n
Calculating the area of a garden to determine how much fertilizer or seed is needed.<\/p>\n<\/div>\n
\n4. Everyday Life:<\/h3>\n
Estimating the size of carpets, curtains, or other household items.<\/p>\n<\/div>\n
Mensuration is a practical skill that helps us measure and understand the world around us.<\/p>\n
Mensuration Quiz – Application Problems<\/h1>\n\n1. Carpet Area: A rectangular room is 5 meters long and 4 meters wide. How much carpet is needed to cover the floor?<\/p>\n
20 sq meters<\/div>\nArea of a rectangle = length \u00d7 width = 5m \u00d7 4m = 20 sq meters.<\/p>\n<\/div>\n<\/div>\n\n2. Garden Fence: A square garden has a side length of 8 meters. How much fencing is needed to enclose the garden?<\/p>\n
32 meters<\/div>\nPerimeter of a square = 4 \u00d7 side = 4 \u00d7 8m = 32 meters.<\/p>\n<\/div>\n<\/div>\n\n3. Triangular Flag: A triangular flag has a base of 1.2 meters and a height of 0.8 meters. What is the area of the flag?<\/p>\n
0.48 sq meters<\/div>\nArea of a triangle = (1\/2) \u00d7 base \u00d7 height = (1\/2) \u00d7 1.2m \u00d7 0.8m = 0.48 sq meters.<\/p>\n<\/div>\n<\/div>\n\n4. Park Design: A park is shaped like a parallelogram with a base of 20 meters and a height of 15 meters. What is the area of the park?<\/p>\n
300 sq meters<\/div>\nArea of a parallelogram = base \u00d7 height = 20m \u00d7 15m = 300 sq meters.<\/p>\n<\/div>\n<\/div>\n\n5. Circular Tablecloth: A circular table has a radius of 1 meter. How much fabric is needed to make a tablecloth for the table (\u03c0 \u2248 3.14)?<\/p>\n
3.14 sq meters<\/div>\nArea of a circle = \u03c0r\u00b2 = 3.14 \u00d7 (1m)\u00b2 = 3.14 sq meters.<\/p>\n<\/div>\n<\/div>\n\n6. Trapezoidal Field: A field is shaped like a trapezium. The two parallel sides are 30 meters and 40 meters long, and the distance between them is 20 meters. What is the area of the field?<\/p>\n
700 sq meters<\/div>\nArea of a trapezium = (1\/2) \u00d7 (sum of parallel sides) \u00d7 height = (1\/2) \u00d7 (30m + 40m) \u00d7 20m = 700 sq meters.<\/p>\n<\/div>\n<\/div>\n\n7. Cube-Shaped Box: A cube-shaped box has a side length of 6 cm. What is the volume of the box?<\/p>\n
216 cubic cm<\/div>\nVolume of a cube = side\u00b3 = 6cm \u00d7 6cm \u00d7 6cm = 216 cubic cm.<\/p>\n<\/div>\n<\/div>\n\n8. Rectangular Tank: A rectangular water tank is 2 meters long, 1.5 meters wide, and 1 meter high. What is the volume of the tank?<\/p>\n
3 cubic meters<\/div>\nVolume of a cuboid = length \u00d7 width \u00d7 height = 2m \u00d7 1.5m \u00d7 1m = 3 cubic meters.<\/p>\n<\/div>\n<\/div>\n\n9. Cylindrical Container: A cylindrical container has a radius of 7 cm and a height of 10 cm. What is the volume of the container (\u03c0 \u2248 3.14)?<\/p>\n
1538.6 cubic cm<\/div>\nVolume of a cylinder = \u03c0r\u00b2h = 3.14 \u00d7 (7cm)\u00b2 \u00d7 10cm = 1538.6 cubic cm.<\/p>\n<\/div>\n<\/div>\n\n10. Swimming Pool: A swimming pool is 20 meters long, 10 meters wide, and has an average depth of 2 meters. What is the volume of water the pool can hold?<\/p>\n
400 cubic meters<\/div>\nVolume = length \u00d7 width \u00d7 depth = 20m \u00d7 10m \u00d7 2m = 400 cubic meters.<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"Mensuration – Class 8 Hi everyone! This chapter is all about Mensuration. We’ll learn how to calculate the areas and volumes of different shapes. These skills are very useful in real life! 1. Area of 2D Shapes a) Rectangle: Area = Length \u00d7 Width Example: A rectangular garden is 10m long and 5m wide. Its […]<\/p>\n","protected":false},"author":1,"featured_media":162663,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/manishchandra.org\/p6\/mathAreaandPerimeterworksheet1.png","fifu_image_alt":"","footnotes":""},"categories":[3,23],"tags":[],"class_list":["post-162649","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-math","cat-3-id","cat-23-id","has_thumb"],"yoast_head":"\n
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1. Construction:<\/h3>\n
Calculating the amount of material needed for building projects (e.g., bricks, cement, paint).<\/p>\n<\/div>\n
2. Packaging:<\/h3>\n
Designing boxes and containers to hold products efficiently.<\/p>\n<\/div>\n
3. Gardening:<\/h3>\n
Calculating the area of a garden to determine how much fertilizer or seed is needed.<\/p>\n<\/div>\n
4. Everyday Life:<\/h3>\n
Estimating the size of carpets, curtains, or other household items.<\/p>\n<\/div>\n
Mensuration is a practical skill that helps us measure and understand the world around us.<\/p>\n
Mensuration Quiz – Application Problems<\/h1>\n\n1. Carpet Area: A rectangular room is 5 meters long and 4 meters wide. How much carpet is needed to cover the floor?<\/p>\n
20 sq meters<\/div>\nArea of a rectangle = length \u00d7 width = 5m \u00d7 4m = 20 sq meters.<\/p>\n<\/div>\n<\/div>\n\n2. Garden Fence: A square garden has a side length of 8 meters. How much fencing is needed to enclose the garden?<\/p>\n
32 meters<\/div>\nPerimeter of a square = 4 \u00d7 side = 4 \u00d7 8m = 32 meters.<\/p>\n<\/div>\n<\/div>\n\n3. Triangular Flag: A triangular flag has a base of 1.2 meters and a height of 0.8 meters. What is the area of the flag?<\/p>\n
0.48 sq meters<\/div>\nArea of a triangle = (1\/2) \u00d7 base \u00d7 height = (1\/2) \u00d7 1.2m \u00d7 0.8m = 0.48 sq meters.<\/p>\n<\/div>\n<\/div>\n\n4. Park Design: A park is shaped like a parallelogram with a base of 20 meters and a height of 15 meters. What is the area of the park?<\/p>\n
300 sq meters<\/div>\nArea of a parallelogram = base \u00d7 height = 20m \u00d7 15m = 300 sq meters.<\/p>\n<\/div>\n<\/div>\n\n5. Circular Tablecloth: A circular table has a radius of 1 meter. How much fabric is needed to make a tablecloth for the table (\u03c0 \u2248 3.14)?<\/p>\n
3.14 sq meters<\/div>\nArea of a circle = \u03c0r\u00b2 = 3.14 \u00d7 (1m)\u00b2 = 3.14 sq meters.<\/p>\n<\/div>\n<\/div>\n\n6. Trapezoidal Field: A field is shaped like a trapezium. The two parallel sides are 30 meters and 40 meters long, and the distance between them is 20 meters. What is the area of the field?<\/p>\n
700 sq meters<\/div>\nArea of a trapezium = (1\/2) \u00d7 (sum of parallel sides) \u00d7 height = (1\/2) \u00d7 (30m + 40m) \u00d7 20m = 700 sq meters.<\/p>\n<\/div>\n<\/div>\n\n7. Cube-Shaped Box: A cube-shaped box has a side length of 6 cm. What is the volume of the box?<\/p>\n
216 cubic cm<\/div>\nVolume of a cube = side\u00b3 = 6cm \u00d7 6cm \u00d7 6cm = 216 cubic cm.<\/p>\n<\/div>\n<\/div>\n\n8. Rectangular Tank: A rectangular water tank is 2 meters long, 1.5 meters wide, and 1 meter high. What is the volume of the tank?<\/p>\n
3 cubic meters<\/div>\nVolume of a cuboid = length \u00d7 width \u00d7 height = 2m \u00d7 1.5m \u00d7 1m = 3 cubic meters.<\/p>\n<\/div>\n<\/div>\n\n9. Cylindrical Container: A cylindrical container has a radius of 7 cm and a height of 10 cm. What is the volume of the container (\u03c0 \u2248 3.14)?<\/p>\n
1538.6 cubic cm<\/div>\nVolume of a cylinder = \u03c0r\u00b2h = 3.14 \u00d7 (7cm)\u00b2 \u00d7 10cm = 1538.6 cubic cm.<\/p>\n<\/div>\n<\/div>\n\n10. Swimming Pool: A swimming pool is 20 meters long, 10 meters wide, and has an average depth of 2 meters. What is the volume of water the pool can hold?<\/p>\n
400 cubic meters<\/div>\nVolume = length \u00d7 width \u00d7 depth = 20m \u00d7 10m \u00d7 2m = 400 cubic meters.<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"Mensuration – Class 8 Hi everyone! This chapter is all about Mensuration. We’ll learn how to calculate the areas and volumes of different shapes. These skills are very useful in real life! 1. Area of 2D Shapes a) Rectangle: Area = Length \u00d7 Width Example: A rectangular garden is 10m long and 5m wide. Its […]<\/p>\n","protected":false},"author":1,"featured_media":162663,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/manishchandra.org\/p6\/mathAreaandPerimeterworksheet1.png","fifu_image_alt":"","footnotes":""},"categories":[3,23],"tags":[],"class_list":["post-162649","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-math","cat-3-id","cat-23-id","has_thumb"],"yoast_head":"\n
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1. Carpet Area: A rectangular room is 5 meters long and 4 meters wide. How much carpet is needed to cover the floor?<\/p>\n
2. Garden Fence: A square garden has a side length of 8 meters. How much fencing is needed to enclose the garden?<\/p>\n
3. Triangular Flag: A triangular flag has a base of 1.2 meters and a height of 0.8 meters. What is the area of the flag?<\/p>\n
4. Park Design: A park is shaped like a parallelogram with a base of 20 meters and a height of 15 meters. What is the area of the park?<\/p>\n
5. Circular Tablecloth: A circular table has a radius of 1 meter. How much fabric is needed to make a tablecloth for the table (\u03c0 \u2248 3.14)?<\/p>\n
6. Trapezoidal Field: A field is shaped like a trapezium. The two parallel sides are 30 meters and 40 meters long, and the distance between them is 20 meters. What is the area of the field?<\/p>\n
7. Cube-Shaped Box: A cube-shaped box has a side length of 6 cm. What is the volume of the box?<\/p>\n
8. Rectangular Tank: A rectangular water tank is 2 meters long, 1.5 meters wide, and 1 meter high. What is the volume of the tank?<\/p>\n
9. Cylindrical Container: A cylindrical container has a radius of 7 cm and a height of 10 cm. What is the volume of the container (\u03c0 \u2248 3.14)?<\/p>\n
10. Swimming Pool: A swimming pool is 20 meters long, 10 meters wide, and has an average depth of 2 meters. What is the volume of water the pool can hold?<\/p>\n
Mensuration – Class 8 Hi everyone! This chapter is all about Mensuration. We’ll learn how to calculate the areas and volumes of different shapes. These skills are very useful in real life! 1. Area of 2D Shapes a) Rectangle: Area = Length \u00d7 Width Example: A rectangular garden is 10m long and 5m wide. Its […]<\/p>\n","protected":false},"author":1,"featured_media":162663,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"https:\/\/manishchandra.org\/p6\/mathAreaandPerimeterworksheet1.png","fifu_image_alt":"","footnotes":""},"categories":[3,23],"tags":[],"class_list":["post-162649","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-math","cat-3-id","cat-23-id","has_thumb"],"yoast_head":"\n