Name the shape ….

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Surface Area of Pyramids

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Presentation transcript:

Name the shape …

Square Based Pyramid ? Ask students to discuss what they might call these 2 measurements. ?

These two lines are perpendicular Square Based Pyramid Height of the pyramid Try to consistently use this terminology – this will make the rest of the lesson much easier Base diagonal These two lines are perpendicular

What do you notice about these 2 lines? Square Based Pyramid Height of the pyramid Right angle – key. Means we can apply Pythagoras Base diagonal What do you notice about these 2 lines?

These two lines are perpendicular Square Based Pyramid Height of the pyramid Right angle – key. Means we can apply Pythagoras Base diagonal These two lines are perpendicular

This means we have a right-angled triangle Square Based Pyramid Height of the pyramid Try to link this back to 3D Pythagoras with the connection to the diagonal in a cuboid Base diagonal This means we have a right-angled triangle

Square Based Pyramid Height of the pyramid Edge length Slant height More terminology – if students haven’t realised we could calculate these lengths, prompt them. Base diagonal Base length

Label any lengths that you know On your wallets … Label any lengths that you know What other information do we need to be able to find the edge length? Base length = 5 cm Some students may go straight through and get the base diagonal Labour the point about half of the base diagonal is the base of triangle 2 5cm

Label any lengths that you know On your wallets … Label any lengths that you know What other information do we need to be able to find the edge length? Base diagonal = 8 cm Working backwards to find side length Again – half the base diagonal to find the base of upright triangle 8cm

Label any lengths that you know On your wallets … Label any lengths that you know What other information do we need to be able to find the edge length? Height = 10 cm 10cm Is there more than one option?

Label any lengths that you know On your wallets … Label any lengths that you know What other information do we need to find the base length ? 10cm Edge length = 10 cm

Label any lengths that you know On your wallets … Label any lengths that you know What other information do we need? Slant height = 10 cm 10cm

A Guyed Radio Mast height = 78 feet Guys are ropes that hold things sturdy. A radio mast is held sturdy with wire guys. How much is guy rope is needed to keep the radio mast in place? 56 feet

How much is guy rope is needed to keep the radio mast in place now? height = 78 feet In 4 equal sections A Guyed Radio Mast It turns out that the radio mast still isn’t sturdy enough so more guy ropes are added. How much is guy rope is needed to keep the radio mast in place now? 56 feet

Challenge: A regular hexagon pyramid is shown. V A regular hexagon pyramid is shown. It has an edge length of 6cm and the base width is 2 cm Calculate the height of the vertex, V , above the hexagon base. 6 cm 2 cm

Create a formula for L in terms of h Challenge 2: Below is a square base pyramid of square base length = 12, height = h, edge length = L Create a formula for L in terms of h