Mathematics
Grade 10
15 min
Area of parallelograms and triangles
Area of parallelograms and triangles
What you'll learn
- Identify the unit rate in a given scenario involving ratios, such as miles per hour or cost per item, with 80% accuracy.
- Solve real-world problems to find equivalent rates using multiplication or division, showing your work clearly, and achieving a correct answer on at least 3 out of 4 problems.
- Explain, in your own words, how unit rates can be used to compare different deals or prices, providing at least two examples.
- Apply knowledge of equivalent rates to create a table showing at least 5 equivalent ratios for a given unit rate.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Derive the area formulas for parallelograms and triangles.
Calculate the area of any parallelogram given its base and corresponding height.
Calculate the area of any triangle given its base and corresponding height.
Apply trigonometric principles to find the area of a parallelogram or triangle when the height is not directly given.
Algebraically solve for a missing dimension (base or height) of a parallelogram or triangle when the area is known.
Solve multi-step problems involving composite figures made of parallelograms and triangles.
Ever wonder how architects calculate the amount of glass needed for a slanted skyscraper facade or how engineers determine forces in a bridge truss? 🏙️ It all starts with mastering the area of parallelograms and triangles!...
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Key Concepts & Vocabulary
TermDefinitionExample
ParallelogramA quadrilateral with two pairs of parallel opposite sides. The opposite sides and opposite angles are equal.A standard rhombus, rectangle, or square. Imagine a rectangle pushed slightly to one side; the resulting shape is a parallelogram.
BaseAny side of a polygon, but typically a side that is oriented horizontally or one to which a height is drawn.In a triangle resting on a flat surface, the side touching the surface is commonly considered the base.
Altitude (Height)A line segment that is perpendicular to the base, drawn from the opposite vertex (for a triangle) or the opposite side (for a parallelogram). Its length is the height.The vertical distance from the peak of a triangular roof straight down to the floor.
AreaThe measure of the two-dimensional s...
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Core Formulas
Area of a Parallelogram
A = b \cdot h
The area (A) of a parallelogram is the product of its base (b) and its corresponding perpendicular height (h). Use this when you know the length of a base and the height that forms a right angle with that base.
Area of a Triangle
A = \frac{1}{2} \cdot b \cdot h
The area (A) of a triangle is one-half the product of its base (b) and its corresponding perpendicular height (h). This formula is derived from the fact that a diagonal divides a parallelogram into two congruent triangles.
Area of a Triangle using Trigonometry
A = \frac{1}{2}ab \cdot \sin(C)
The area (A) of a triangle is one-half the product of the lengths of two sides (a and b) and the sine of their included angle (C). This is extremely useful when the perpendicular heigh...
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Challenging
The area of a triangle is 96 cm². The lengths of two of its sides are 16 cm and 20 cm. What is the sine of the included angle between these two sides?
A.0.5
B.0.8
C.0.6
D.1.2
Challenging
A rhombus is a type of parallelogram with four equal sides. If a rhombus has a side length of 10 units and one of its interior angles is 45°, what is its area?
A.100 units²
B.50√2 units²
C.50 units²
D.100√2 units²
Challenging
Why is the area of a parallelogram calculated as base times PERPENDICULAR height (b*h) and not base times slant height (b*s)?
A.Because the Pythagorean theorem only works with perpendicular lines.
B.Because it is a convention that is easier to remember.
C.Because a parallelogram can be rearranged into a rectangle with sides 'b' and 'h', and the area of that rectangle is b*h.
D.Because the slant height is always longer, which would make the area too large.
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Frequently asked questions
What grade level is "Area of parallelograms and triangles"?
Area of parallelograms and triangles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Area of parallelograms and triangles?
You'll be able to: Identify the unit rate in a given scenario involving ratios, such as miles per hour or cost per item, with 80% accuracy; Solve real-world problems to find equivalent rates using multiplication or division, showing your work….
Is "Area of parallelograms and triangles" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Area of parallelograms and triangles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.