Mathematics: Equations and Area Calculations

What is the value of y when $x = 12$ in the equation $y = x + 26$?

If $b = 20$ cm and $h = 45$ cm, then the area of the triangle is 450 cm².

What is the formula for the average A of four numbers m, n, p, and q?

The formula for the product P of three numbers x, y, and z is P = ______.

Match the following formulas with their description:

Find y when x = 12, y = x + 26

Find a when x = 2, y = -1, and z = -3, a= (y^2 - xz)/5

Find area of triangle, A = 1/2bh, b = 20cm, h = 45cm

Find height (h) of triangle, A=30cm^2, b=10cm, A = (1/2)bh

Formula for average A of four numbers m,n,p,q

Exercise 5B

Basic Level
- If y = x + 26, find y when x = 12. y = 38
- If a = (y² - xz)/5, find a when x = 2, y = -1, and z = -3. a = 1
- If S = 4πr², find S when r = 10½. S = 1386
- Find the positive value of r when S = 616. r = 14
Intermediate Level
- If k = p + 2q, find p when k = 7 and q = 9. p = -11
- If U = πr(r+h), find r when U = 16 and h=2. (π is ~22/7) r = 2
- If v² = u² + 2gs, find s when v = 25, u = 12 and g = 10. s = 2.5.
- If (1/a) - (1/b) = (1/c) and a = 3, b = 4, and d = -5, find c. c = -12
- If (1/c) = (1/a) + (1/b) + (1/d), find c when a = 1/1, b = 1/2 and d=1/4. c=1/5

Triangle Area

The area of a triangle is calculated using the formula: A = ½bh where b is the base length and h is the height respectively.
- If the base is 20 cm and the height is 45 cm, calculate A? A = 450 cm²
- If the area is 30 cm² and the base is 10 cm, find the height? h = 6 cm

Other Formulas

Product P of three numbers x, y and z = xyz
Sum S of the square of p and the cube of q = p² + q³
Average A of four numbers m, n, p and q = (m+n+p+q)/4
Time T, in minutes, for a train journey of a hours b minutes = 60a +b

Test your skills with this quiz on basic and intermediate level mathematical equations, including finding values for variables and calculating the area of triangles. Solve problems involving algebraic formulas and geometry to reinforce your understanding of these concepts.