I can find the surface area of a pyramid by adding the base area and the lateral faces.Puedo hallar el área de superficie de una pirámide sumando el área de la base y las caras laterales.
MissionMisión · Orbit StationEstación orbital · night shiftturno de noche
Mission control needs your math.El control de la misión necesita tus matemáticas.
A debris warning changes the plan: some beacons lose their base panel, and some measurements arrive as heights instead of slant heights. Check what each beacon needs before ordering.
Una alerta de escombros cambia el plan: algunas balizas pierden su panel de base y algunas medidas llegan como alturas en lugar de alturas inclinadas. Revisa lo que necesita cada baliza antes de hacer el pedido.
Word bankBanco de palabras 5 words5 palabraspyramid, slant height, lateral face, …pirámide, altura inclinada (apotema), cara lateral, …
- pyramidpirámide
- A solid with one base and triangle sides that meet at one point.Un sólido con una base y lados triangulares que se unen en un punto.
- slant heightaltura inclinada (apotema)
- The height of a side triangle, measured along the slanted face.La altura de un triángulo lateral, medida a lo largo de la cara inclinada.
- lateral facecara lateral
- A triangle side of a pyramid, not the base.Un lado triangular de una pirámide, no la base.
- basebase
- The flat bottom of a pyramid.El fondo plano de una pirámide.
- apexápice
- The point at the top where the sides of a pyramid meet.El punto de arriba donde se unen los lados de una pirámide.
Stage 1 of 5Etapa 1 de 5
Start StrongEmpieza fuerte
Each rung is harder than the last, and the numbers change every time.
Cada peldaño es más difícil que el anterior y los números cambian cada vez.
- 6 fresh problems with new numbers each time (interactive only).
Stage 2 of 5Etapa 2 de 5
Stretch Your ThinkingAmplía tu pensamiento
Plan, solve, then check that your answer makes sense.
Planea, resuelve y revisa que tu respuesta tenga sentido.
- Find the Surface Area Error
- Two pyramids have the same base area (64 in²) but different slant heights. Pyramid A has slant height 6 in and Pyramid B has slant height 10 in. How much more surface area does Pyramid B have? Why does slant height affect surface area but NOT base area?
- Fill in the table
- A square pyramid beacon has a base 10 m on each side and is 12 m tall. Each of its four triangular panels has a base of 10 m and a slant height of 13 m. How many square meters do the four panels cover?
- 260 m²
- 240 m²
- 360 m²
- 130 m²
- Orbit Station is comparing three square-pyramid beacons. Fill in the missing areas for each beacon, in square meters.
- A square pyramid beacon has a base 8 m on each side. Its four triangular panels cover 96 m² altogether. What is the slant height of each panel?
- A pyramid has a triangular base with sides of 6 m and a height of 5.2 m (rounded). Its 3 triangular sides each have a base of 6 m and a slant height of 7 m. What is the approximate total surface area?
- 63 m²
- 99.6 m²
- 157.2 m²
- 78.6 m²
Stage 3 of 5Etapa 3 de 5
InvestigateInvestiga
Use the model to test an idea. Then check it.
Usa el modelo para probar una idea. Luego compruébala.
- A square pyramid has a base edge and a slant height given. Sort each measurement by whether you need it to find the surface area.
- Match each square-pyramid beacon to its total surface area.
- A square pyramid has a base edge of 4 m and a total surface area of 48 m². Tap the slant height of its triangular sides, in meters.
- Make a wrapping plan for a square pyramid gift box. Choose a base side and a slant height. Draw a net, label the base and one triangular face, and find the total wrap. Explain why slant height is not the same as the pyramid's height.
- 2 fresh problems with new numbers each time (interactive only).
Stage 4 of 5Etapa 4 de 5
Find and FixEncuentra y corrige
Somebody made a mistake. Find the step and fix it.
Alguien cometió un error. Encuentra el paso y corrígelo.
- Ilsa finds the surface area of a square pyramid with a base edge of 9 m and a slant height of 7 m. Tap the step where her work first goes wrong.
- Kofi finds the surface area of a square pyramid with a base edge of 10 cm, a vertical height of 12 cm and a slant height of 13 cm. Tap the step where his work first goes wrong.
- Mina finds the surface area of a square pyramid with a base edge of 14 in and a slant height of 5 in. Tap the step where her work first goes wrong.
- Pyramids A and B have the same 6 m by 6 m square base. A has a slant height of 5 m. B has a slant height of 8 m. Dev says they have equal surface areas because the bases are the same. Mira says B has more. Who is right?
- Dev, because the base is part of the surface area
- Dev, because the pyramids have the same number of faces
- Mira, because B's triangular sides are bigger
- Mira, because B has a bigger base
- What is the best next move?
- Add one triangle to the base: 36 + 15.
- Redo each triangle with the vertical height: ½ × 6 × 4.
- Multiply the base by one triangle: 36 × 15.
- Multiply 15 by the number of triangle faces, then add the base.
- 2 fresh problems with new numbers each time (interactive only).
Stage 5 of 5Etapa 5 de 5
Prove Your UnderstandingDemuestra tu comprensión
Say how sure you are, solve, then create a problem of your own.
Di qué tan seguro estás, resuelve y luego crea un problema tuyo.
- A square pyramid has a base edge of 7 cm and a slant height of 12 cm. What is its total surface area?
- A square pyramid has a base edge of 10 m, a vertical height of 12 m and a slant height of 13 m. Which length is the height of each triangular side when you find its area?
- 12 m
- 13 m
- 10 m
- 5 m
- A square pyramid has a base edge of 9 ft and a slant height of 11 ft. Which expression gives its total surface area in square feet?
- 4 × (½ × 9 × 11)
- 9 × 9 + ½ × 9 × 11
- 9 × 9 × 11
- 9² + 4(9 × 11 ÷ 2)
- A square pyramid dust cover has a base edge of 6 ft and a slant height of 10 ft. The bottom is open and needs no fabric. How many square feet of fabric cover the sloping sides?
- Foil for a pyramid-shaped satellite shield costs $3 per square meter. The shield is a square pyramid with a base edge of 8 m and a slant height of 5 m, and every face gets foil. How much does the foil cost?
- $432
- $240
- $144
- $192
- Create your own Orbit Station beacon problem. Choose a square pyramid, give its base edge and slant height, and find its surface area. Explain which parts you added and why.