A focused Grade 6 learning session for Area of Triangles using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving area of triangles.
Area of Triangles means measuring how much flat space a figure covers by using equal-sized square units.
Question: What is the area of a triangle with base \(10\) cm and height \(6\) cm?
Why it works: Area of a triangle \(=\frac{1}{2}\times b\times h=\frac{1}{2}\times10\times6=30\) cm\(^2\).
Answer: \(30\) cm\(^2\)
Question: A right triangle has legs of length \(5\) m and \(12\) m. What is its area?
Answer: \(30\) m\(^2\)
Question: An isosceles triangle has a base of \(14\) cm. A perpendicular line from the top vertex to the base has length \(9\) cm. What is the area?
Answer: \(63\) cm\(^2\)
Question: A triangular flag has an area of \(36\) in\(^2\) and a height of \(9\) inches. What is its base?
Why it works: \(36=\frac{1}{2}\times b\times 9 \Rightarrow b=8\) in.
Answer: \(8\) in
Area of Triangles becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Area means every square unit inside the figure.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is the area of a triangle with base \(10\) cm and height \(6\) cm?
Answer B: \(30\) cm\(^2\)
Area of a triangle \(=\frac{1}{2}\times b\times h=\frac{1}{2}\times10\times6=30\) cm\(^2\).
A triangle has a base of \(8\) inches and a height of \(4\) inches. What is its area?
Answer D: \(16\) in\(^2\)
Using \(A=\frac{1}{2}bh\), we get \(A=\frac{1}{2}\times 8\times 4=16\) in\(^2\).
Which formula correctly finds the area of a triangle?
Answer C: \(A=\frac{1}{2}bh\)
The area formula for any triangle is \(A=\frac{1}{2}bh\), where \(b\) is base and \(h\) is height.
A right triangle has legs of length \(5\) m and \(12\) m. What is its area?
Answer B: \(30\) m\(^2\)
For a right triangle, \(A=\frac{1}{2}\times 5\times 12=30\) m\(^2\).
An isosceles triangle has a base of \(14\) cm. A perpendicular line from the top vertex to the base has length \(9\) cm. What is the area?
Answer D: \(63\) cm\(^2\)
\(A=\frac{1}{2}\times 14\times 9=63\) cm\(^2\).
What is the height of a triangle with area \(24\) ft\(^2\) and base \(8\) ft?
Answer B: \(6\) ft
Rearranging \(A=\frac{1}{2}bh\): \(24=\frac{1}{2}\times 8\times h \Rightarrow h=6\) ft.
Find the base of a triangle with area \(45\) m\(^2\) and height \(10\) m.
Answer D: \(9\) m
Solving \(45=\frac{1}{2}\times b\times 10 \Rightarrow b=9\) m.
An obtuse triangle has a base of \(15\) inches and a perpendicular height of \(8\) inches measured from the opposite vertex to the extended base line. What is the area?
Answer A: \(60\) in\(^2\)
Even for obtuse triangles, \(A=\frac{1}{2}bh=\frac{1}{2}\times 15\times 8=60\) in\(^2\).
Identify the height in the triangle shown. The height must be perpendicular to the base.
Answer C: \(7\) cm
The height is the perpendicular distance from the base to the opposite vertex, shown by the dashed line as \(7\) cm.
A triangular flag has an area of \(36\) in\(^2\) and a height of \(9\) inches. What is its base?
Answer B: \(8\) in
\(36=\frac{1}{2}\times b\times 9 \Rightarrow b=8\) in.
Which statement about the height of a triangle is true?
Answer D: It is always perpendicular to the base.
The height is defined as the perpendicular distance from the base to the opposite vertex, regardless of the triangle type.
