Determine the Area of Triangles
Name Period
Objectives / Objetivos
Content Objective: I can find the area of a triangle using the formula A = ½ × base × height.
Language Objective: I can explain my steps using the words base, height, area, and perpendicular.
Key Idea / Idea clave
Area of Triangles. Formula: Area = ½ × Base × Height (A = ½ b · h). 1. Identify the base and the perpendicular height to that base. 2. A triangle is exactly half of a rectangle with the same base and height. 3. Multiply base by height, then divide by 2
I Notice / Observo
- What shape are the garden beds?
- What measurements do we need to find the area?
I Wonder / Me pregunto
- Why do we divide by 2 when finding the area of a triangle?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Area of a Triangle Área de un triángulo | The space inside a triangle. A triangle is half of a rectangle with the same base and height, so A = ½ × b × h. El espacio dentro de un triángulo. Un triángulo es la mitad de un rectángulo con la misma base y altura, por eso A = ½ × b × h. |
| Base Base | Any side of a triangle can be the base. Once you pick a base, the height must be measured perpendicular (at a 90° angle) to it. Cualquier lado de un triángulo puede ser la base. Una vez que eliges la base, la altura debe medirse perpendicular (en un ángulo de 90°) a ella. |
| Height Altura | The straight-up distance from the base to the top corner. La distancia recta desde la base hasta la esquina de arriba. |
| Area Área | How much space is inside a flat shape. Cuánto espacio hay dentro de una figura plana. |
| Perpendicular Perpendicular | Two lines that meet to make a square corner (90 degrees). Dos líneas que se unen formando una esquina recta (90 grados). |
| Composite figure Figura compuesta | A shape made by putting two or more simple shapes together. Una figura formada al juntar dos o más figuras simples. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. What is the area of a triangle with base 10 cm and height 6 cm?
- A 16 sq cm
- B 30 sq cm
- C 30 cm
- D 60 sq cm
Answer:
2.
Complete each empty cell. Show your reasoning below.
| Triangle | Base | Height | Area |
|---|---|---|---|
| Garden A | 12 ft | 8 ft | |
| Garden B | 9 ft | 27 sq ft | |
| Garden C | 10 ft | 35 sq ft | |
| Garden D | 15 ft | 4 ft |
3. Match each shape to its area. Watch the rule: triangles use A = ½ × base × height, but parallelograms and rectangles use A = base × height (do NOT take half).
Write the letter of the matching item in the blank.
| 1. | Triangle b=8, h=6 | A. | 21 sq units | |
| 2. | Triangle b=10, h=8 | B. | 20 sq units | |
| 3. | Triangle b=12, h=5 | C. | 40 sq units | |
| 4. | Parallelogram b=5, h=4 | D. | 30 sq units | |
| 5. | Rectangle 7×3 | E. | 18 sq units | |
| 6. | Parallelogram b=9, h=2 | F. | 24 sq units |
4. Find the Area Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: