I can find the area of a regular polygon by decomposing it into triangles.Puedo hallar el área de un polígono regular descomponiéndolo en triángulos.
MissionMisión · Robot LabLaboratorio de robots · night shiftturno de noche
Test, measure, improve.Prueba, mide, mejora.
Overnight the lab's plans change: some measurements arrive backward, and every height is rounded. Check each plate before the robots start tiling.
Durante la noche cambian los planos del laboratorio: algunas medidas llegan al revés y todas las alturas están redondeadas. Revisa cada placa antes de que los robots empiecen a colocar baldosas.
Word bankBanco de palabras 5 words5 palabrasregular polygon, decompose, triangle, …polígono regular, descomponer, triángulo, …
- regular polygonpolígono regular
- A flat shape with straight sides where all sides are equal and all angles are equal.Una figura plana de lados rectos donde todos los lados y todos los ángulos son iguales.
- decomposedescomponer
- To break a shape into smaller, simpler shapes.Separar una figura en figuras más pequeñas y simples.
- triangletriángulo
- A shape with three sides. Its area is ½ × base × height.Una figura de tres lados. Su área es ½ × base × altura.
- compositecompuesto
- Made by putting two or more simple shapes together.Formado al juntar dos o más figuras simples.
- formulafórmula
- A math rule written with symbols.Una regla matemática escrita con símbolos.
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 Area Error (use rounded heights)
- A regular hexagon and a regular pentagon are each divided into congruent central triangles. In both polygons, each central triangle has area 15 sq ft. Which polygon has greater total area? Explain why the triangle count matters. The two polygons have different side lengths.
- Use total area = number of triangles × ½ × base × height to find each missing value. Nonsquare measurements are rounded; use the displayed values.
- Each sensor plate is a regular hexagon with sides of 20 cm. Its 6 center triangles each have a height of 17.3 cm (rounded). One sheet of film covers 400 cm². How many sheets cover 4 plates?
- 11 sheets
- 10 sheets
- 3 sheets
- 21 sheets
- Robot Lab is comparing three regular-polygon floor plates. Fill in the area of one triangle and the area of each plate, in square feet. Use the given heights; they are rounded, so areas with decimals are estimates.
- A regular pentagon pad is split from its center into 5 identical triangles. Each triangle has a base of 10 ft, and the whole pad has an area of 172.5 ft². What is the height of each triangle?
- A regular hexagon charging pad has a perimeter of 48 ft. Split from the center, each triangle has a height of 6.9 ft (rounded). What is the approximate area of the pad?
- 165.6 ft²
- 27.6 ft²
- 331.2 ft²
- 110.4 ft²
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.
- Sort each statement about finding the area of a regular polygon: true or false?
- Match each regular polygon to its total area. Use the given heights.
- A regular hexagon has an area of 54 cm² and splits into 6 identical triangles. Tap the area of one triangle, in square centimeters.
- Design a regular polygon floor for the pavilion. Choose the number of sides and the side length. Use the model to read the height of one triangle, and round it to the nearest tenth. Sketch how the floor splits into congruent triangles, find the area of one, and then find the total area.
- 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.
- Ivo finds the area of a regular hexagon whose center triangles have a base of 12 in and a height of 10.4 in (rounded). Tap the step where his work first goes wrong.
- Noor finds the area of a regular octagon whose 8 center triangles each have a base of 8 cm and a height of 9.7 cm (rounded). Tap the step where her work first goes wrong.
- Diego finds the area of a regular hexagon whose center triangles have a base of 9 m and a height of 7.8 m (rounded). Tap the step where his work first goes wrong.
- A regular hexagon has sides of 6 ft. Li says to use 6 ft as the height of each center triangle. Omar says the height is the distance from the center straight to a side, which is 5.2 ft (rounded). Who is right?
- Li, because the side is the longest length in the triangle
- Both, because either length works for the area
- Omar; triangle height meets its base at a right angle.
- Neither, because the height is half of the side, 3 ft
- What is the best next move?
- Multiply 21.6 by 8, one for each side.
- Add 21.6 + 8.
- Stop, because 21.6 in² is the area of the octagon.
- Multiply 21.6 by 6, the length of a side.
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 regular pentagon is split from its center into 5 identical triangles. Each triangle has a base of 14 cm and a height of 9.6 cm (rounded). What is the approximate area of the pentagon?
- A regular polygon floor has an area of 144 ft² and splits into identical triangles of 18 ft² each. Which polygon is it?
- A regular hexagon
- A regular decagon
- A regular pentagon
- A regular octagon
- A regular decagon robot pad has 10 center triangles, each with a base of 4 ft and a height of 6.2 ft (rounded). Special coating costs $5 per square foot. How much does it cost to coat the whole pad?
- Regular hexagon plate A has 6 center triangles of 14 ft² each. Regular pentagon plate B has 5 center triangles of 17 ft² each. Which plate has the greater area, and by how much?
- Plate A, because it has more triangles
- Plate B, by 1 ft²
- Plate B, by 3 ft²
- They have the same area
- A regular hexagon has center triangles with a base of 6 ft and a height of 5.2 ft. Which expression gives the area of the hexagon in square feet?
- 6 × (½ × 6 × 5.2)
- ½ × 6 × 5.2
- 6 + ½ × 6 × 5.2
- 6 × 6 × 5.2
- Create your own Robot Lab plate problem. Choose a regular polygon, give the base and height of its center triangles, and find its area. Explain how you know how many triangles there are.