I can find the area of a composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas.Puedo hallar el área de una figura compuesta descomponiéndola en figuras básicas, incluido un polígono regular dividido en triángulos, y sumando o restando las áreas.
MissionMisión · Pixel ArcadeArcade de píxeles · night shiftturno de noche
Clear every level.Supera todos los niveles.
Bonus round after closing: the arcade owner left rough sketches of new rooms, with pits, notches and slanted roofs. Decompose each one carefully, because the carpet order is final.
Ronda extra después del cierre: el dueño del arcade dejó bocetos de salas nuevas, con huecos, muescas y techos inclinados. Descompón cada una con cuidado, porque el pedido de alfombra es definitivo.
Word bankBanco de palabras 4 words4 palabrascomposite figure, decompose, congruent, …figura compuesta, descomponer, congruente, …
- composite figurefigura compuesta
- A shape made by putting two or more simple shapes together.Una figura formada al juntar dos o más figuras simples.
- decomposedescomponer
- To break a shape into smaller, simpler shapes.Separar una figura en figuras más pequeñas y simples.
- congruentcongruente
- Exactly the same size and shape.Exactamente del mismo tamaño y forma.
- regular polygonpolígono regular
- A shape whose sides are all the same length and whose angles are all the same size.Una figura cuyos lados tienen la misma longitud y cuyos ángulos tienen la misma medida.
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
- A T-shaped room can be decomposed in two different ways. Show both ways and prove they give the same total area. Use a T-shape where the top is 14 ft × 4 ft and the stem is 6 ft × 10 ft.
- Fill in the table
- Each grid square is 1 ft. This L-shaped floor is a 12 ft by 5 ft rectangle with a 5 ft by 4 ft rectangle on top. Carpet costs $6 per square foot. How many dollars does the carpet cost?
- A prize wall is 14 ft wide and 9 ft tall. It has a 4 ft by 3 ft window and a 3 ft by 7 ft door cut out of it. How many square feet of the wall can be painted?
- 93 ft²
- 105 ft²
- 114 ft²
- 159 ft²
- A game cabinet side panel is made of A, a 9 ft by 6 ft rectangle; B, a triangle on top with base 9 ft and height 4 ft; and C, a 4 ft by 3 ft rectangular screen cut out. Find each area, then the panel area A + B − C.
- A sign is a regular octagon. Its 8 identical triangles meet at the center. Each has a base of 6 in and a height of 7 in. What is the area of the whole sign, in square inches?
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.
- Match each arcade floor plan to its total area.
- Sketch a festival floor made of a trapezoid and a rectangle joined together. Label enough measurements to find its total area. Then show a second, different way to decompose the same floor and check that both give the same area.
- 4 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.
- A clubhouse wall is an 18 ft by 11 ft rectangle with a triangle on top that has a base of 18 ft and a height of 6 ft. Dana finds the total area. Tap the first step where her work goes wrong.
- A 16 ft by 9 ft game room has a 4 ft by 5 ft supply closet cut out of one corner. Eli finds the usable floor area. Tap the first step where his work goes wrong.
- An arcade stage is a 10 ft by 8 ft rectangle with a triangle on its 10 ft side. The triangle has a base of 10 ft and a height of 4 ft. Fay finds the area. Tap the first step where her work goes wrong.
- Mo and Ana each cut an L-shaped floor into two rectangles. Each grid square is 1 ft. Mo cuts a 10 by 4 and a 4 by 6. Ana cuts a 4 by 10 and a 6 by 4. Who gets the correct area?
- Only Mo, because he cut the bottom first
- Only Ana, because her rectangles are taller
- Both. Each way gives 64 ft².
- Neither, because their areas are different
- What is the best next move?
- Add the 2 m by 3 m pad: 106 + 2 × 3.
- Subtract 2 and 3 from 106.
- Stop, because 106 m² is the answer.
- Subtract the 2 m by 3 m pad: 106 − 2 × 3.
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.
- An L-shaped arcade lounge is made of a 14 ft by 6 ft rectangle and a 5 ft by 4 ft rectangle joined to it. What is the total area, in square feet?
- A 16 m by 12 m courtyard has a square fountain, 4 m on each side, cut out of it. What is the area left for visitors?
- 16 m²
- 192 m²
- 208 m²
- 176 m²
- A hexagon-shaped prize table is a regular hexagon. It splits into 6 identical triangles. Each triangle has a base of 10 cm and a height of 9 cm. What is the area of its top surface, in square centimeters?
- A game booth front is a 10 ft by 8 ft rectangle with a triangular roof on top. The triangle's base is 10 ft. The whole front has an area of 140 ft². What is the height of the triangular roof, in feet?
- A 12 ft by 8 ft arcade room has a 4 ft by 3 ft notch cut out of one corner. Which expression gives the floor area?
- 12 × 8 + 4 × 3
- 12 × 8 − 4 × 3
- (12 − 4) × (8 − 3)
- 12 × 8 × 4 × 3
- Create your own Pixel Arcade composite figure. Describe a floor or wall made of two or three simple shapes, find its area, and explain whether you add or subtract each piece.