Geometric Area and Perimeter Problems

The video tutorial covers solving geometric problems involving rectangles, rhombuses, playgrounds, squares, polygons, hexagons, and square poles with footpaths. It demonstrates how to use area formulas and relationships between dimensions to find unknown lengths, widths, and sides. The tutorial also explains solving quadratic equations to determine these dimensions.

If the length of a rectangle is 2 cm more than its breadth and the area is 24 cm², what is the length of the rectangle?

• 7 cm

• 4 cm

• 5 cm

• 6 cm

Given a rhombus where one diagonal is 4 cm less than the other and the area is 30 cm², what is the length of the longer diagonal?

• 8 cm

• 6 cm

• 12 cm

• 10 cm

A rectangular playground has an area of 420 m². If its length is increased by 7 m and breadth decreased by 5 m, what is the new length?

• 18 m

• 19 m

• 21 m

• 20 m

The sum of the areas of two squares is 400 m², and the difference in their perimeters is 16 m. What is the side length of the larger square?

• 16 m

• 12 m

• 14 m

• 18 m

If the exterior angle of a polygon with n sides is 500 more than that of a polygon with n² sides, what is the number of sides of the first polygon?

• 6

• 7

• 5

• 4

The side of one regular hexagon is 1 cm more than another, and the product of their areas is 243. What is the side length of the smaller hexagon?

• 1 cm

• 2 cm

• 4 cm

• 3 cm

A square pole has a footpath of width 2 m around it, and the area of the footpath is 5/4 times that of the pole. What is the area of the pole?

• 81 m²

• 36 m²

• 49 m²

• 64 m²