Question

area, volume and capacity
topic 3: area of a triangle
question 1 find the area of the following triangles.
question 2
a a triangle has a base of 30 cm and a height of 15 cm. what is its area?
b a triangle has an area of 112 cm² and a base length of 28 cm. find its height.
question 3 find the area of the triangles whose base and height are given.
question 4 complete the following. (all lengths are in cm; areas are in cm².)

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Solve Question 2a

Given \(base = 30\space cm\) and \(height=15\space cm\).
Substitute into the formula: \(A=\frac{1}{2}\times30\times15\).
First, calculate \(30\times15 = 450\).
Then, \(\frac{1}{2}\times450=225\space cm^{2}\).

Step3: Solve Question 2b

Given \(A = 112\space cm^{2}\) and \(base = 28\space cm\).
From the formula \(A=\frac{1}{2}\times base\times height\), we can solve for \(height\).
Rearrange the formula to \(height=\frac{2A}{base}\).
Substitute \(A = 112\) and \(base = 28\): \(height=\frac{2\times112}{28}\).
First, calculate \(2\times112 = 224\).
Then, \(\frac{224}{28}=8\space cm\).

Answer:

Question 2a: \(225\space cm^{2}\)
Question 2b: \(8\space cm\)