I can find the area of a triangle using the formula A = ½ × base × height.Puedo hallar el área de un triángulo usando la fórmula A = ½ × base × altura.
MissionMisión · Harbor WorksPuerto de trabajo · night shiftturno de noche
Keep the port running.Mantén el puerto en marcha.
Night shift at the harbor: fog rolls in, and the lighthouse crew needs new triangular signal sails by sunrise. Find every area carefully, because a wrong cut wastes cloth you cannot replace.
Turno de noche en el puerto: llega la niebla y el equipo del faro necesita nuevas velas de señales triangulares al amanecer. Halla cada área con cuidado, porque un corte equivocado desperdicia tela que no se puede reponer.
Word bankBanco de palabras 4 words4 palabrastriangle, base, height, …triángulo, base, altura, …
- triangletriángulo
- A shape with three sides. Its area is half of a rectangle with the same base and height.Una figura con tres lados. Su área es la mitad de un rectángulo con la misma base y altura.
- basebase
- Any side of a triangle. The height is measured perpendicular to it.Cualquier lado de un triángulo. La altura se mide perpendicular a ella.
- heightaltura
- The straight distance from the base to the opposite corner, at a right angle to the base.La distancia recta desde la base hasta la esquina opuesta, en ángulo recto con la base.
- perpendicularperpendicular
- Meeting to make a square corner of 90 degrees.Que se cruza formando una esquina cuadrada de 90 grados.
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 rectangle is 12 ft by 8 ft. A diagonal line cuts it into two triangles. What is the area of each triangle? Explain how the triangle area formula relates to the rectangle area formula.
- A harbor tug flies a triangular sail with a base of 6 m and a height of 9 m. Sailcloth costs $12 per square meter. How many dollars does the cloth for one sail cost?
- A triangular signal flag has an area of 54 cm² and a base of 12 cm. What is its height?
- 4.5 cm
- 9 cm
- 42 cm
- 108 cm
- Three warning pennants are triangles. Find each missing value, then add the three areas in the Total row.
- Triangle P has a base of 10 m and a height of 8 m. Triangle Q has the same area as P and a base of 16 m. What is the height of Triangle Q?
- 2.5 m
- 8 m
- 5 m
- 80 m
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.
- The harbor inspector reads out claims about triangles. Sort each claim as true or false.
- Design one triangular garden and one parallelogram garden with exactly the same area. Label each base and perpendicular height, and explain where the factor of one half belongs.
- 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 harbor sail has a base of 16 ft and a height of 9 ft. Yara finds its area. Tap the first step where her work goes wrong.
- A sail is a right triangle. Its base is 8 m, its height is 6 m, and its sloping edge is 10 m. Teo finds its area. Tap the first step where his work goes wrong.
- A triangular tarp has an area of 30 ft² and a base of 10 ft. Mina finds its height. Tap the first step where her work goes wrong.
- A right triangle has legs of 6 m and 8 m. Sana says its area changes depending on which side you pick as the base. Joon says the area stays the same if you use the matching height. Who is right?
- Joon; both matching base-height pairs give 24 m².
- Sana. A different base gives a different area.
- Neither. Only the longest side can be the base.
- Both. The area is 24 m² with one base and 48 m² with the other.
- What is the best next move?
- Use the 15 cm side as the base and the 9 cm side as the height.
- Use the 9 cm and 12 cm sides as the base and the height.
- Add the three sides: 9 + 12 + 15.
- Multiply all three sides, 9 × 12 × 15, and take half.
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 signal flag at Harbor Works is a triangle with a base of 14 ft and a height of 9 ft. What is its area, in square feet?
- A rectangular tarp is 12 m long and 8 m wide. The crew cuts it along one diagonal into two equal triangles. What is the area of one triangle?
- 20 m²
- 24 m²
- 96 m²
- 48 m²
- A triangular sail has an area of 70 cm² on a scale model. Its height is 10 cm. What is the length of its base, in centimeters?
- Flag A has a base of 9 ft and a height of 8 ft. Flag B has a base of 12 ft and a height of 5 ft. Which flag has the greater area, and by how much?
- Flag B, because its base is longer
- Flag A, by 6 ft²
- Flag A, by 12 ft²
- They have equal areas
- A triangular warning sign has a base of 18 ft and a height of 10 ft. One can of paint covers 40 ft². How many cans must the crew buy to paint one side of the sign?
- Create your own Harbor Works problem about the area of a triangle. Give a base and a height, find the area, and explain why the formula has a one-half.