Surface Area and Triangle Area Calculations

This video tutorial covers the calculation of surface areas for square-based and rectangular-based pyramids. It begins with an introduction to the concept, followed by step-by-step examples. The tutorial includes calculations using basic geometry and Pythagoras' theorem to find the surface area of different pyramid types. The video concludes with a summary of the methods discussed.

What is the first step in calculating the surface area of a square-based pyramid?

• Calculate the volume of the pyramid

• Find the perimeter of the base

• Draw the net of the pyramid

• Measure the height of the pyramid

How do you calculate the area of one triangle in a square-based pyramid with a base of 5 cm and height of 4 cm?

• 5 + 4

• 5 x 4

• 5 x 4 x 2

• 5 x 4 / 2

What is the total surface area of a square-based pyramid with a base area of 25 cm² and four triangles each with an area of 10 cm²?

• 45 cm²

• 55 cm²

• 65 cm²

• 75 cm²

In a rectangular-based pyramid, what is the area of a rectangle with dimensions 8 cm by 6 cm?

• 28 cm²

• 14 cm²

• 48 cm²

• 64 cm²

How do you calculate the area of a triangle with a base of 6 cm and height of 5 cm?

• 6 x 5

• 6 x 5 / 2

• 6 + 5

• 6 x 5 x 2

What is the total surface area of a rectangular-based pyramid with a rectangle area of 48 cm² and two sets of triangles with areas 15 cm² and 16.8 cm² each?

• 131.6 cm²

• 111.6 cm²

• 141.6 cm²

• 121.6 cm²

What theorem is used to find the hypotenuse of a triangle in a rectangular-based pyramid?

• Archimedes' theorem

• Thales' theorem

• Euclid's theorem

• Pythagoras' theorem

If a triangle in a rectangular-based pyramid has a base of 3.5 cm and a height of 3.5 cm, what is the length of the hypotenuse?

• 4.5 cm

• 4.9 cm

• 5.5 cm

• 5.9 cm

What is the area of a triangle with a base of 4 cm and a height of 4.9 cm?

• 9.8 cm²

• 10.8 cm²

• 11.8 cm²

• 12.8 cm²

What is the total surface area of a rectangular-based pyramid with a rectangle area of 28 cm² and two sets of triangles with areas 14 cm² and 9.8 cm² each?

• 65.6 cm²

• 85.6 cm²

• 75.6 cm²

• 95.6 cm²