Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# What might be the values of H, A and B in this trapezium, when the area is 432 cm2? ? Relevance
• Here's my guess from the dimensions of the picture:

h = 16 cm

a = 18 cm

b = 36 cm

But it could be almost anything. The key is that the height times the *average* of the bases must be 432.

Double-checking my set of numbers:

16 * (18 + 36)/2

16 * 27

= 432 cm²

Just for the sake of showing the answer can't be unique, here's another set of values:

h = 12 cm

a = 30 cm

b = 42 cm

12 * (30 + 42)/2

12 * 36

= 432 cm²

And one more:

h = 18 cm

a = 16 cm

b = 32 cm

18 * (16 + 32)/2

18 * 24

= 432 cm²

• There are many answers, but they are probably wanting you to factor out an expression to come up with integer possible outcomes.

Starting with the equation for the area of a trapezoid:

A = (a + b)h / 2

We know the area is 432 cm², so:

432 = (a + b)h / 2

Multiply both sides by 2:

864 = (a + b)h

Now let's get a prime factorization of 864 to come up with two values that we can use to multiply to get that number:

864 = 2⁵ * 3³

So we can just use those values:

864 = 32 * 27

So if we say h = 27, then we need (a + b) to be 32.  Making any two values that total 32 will work.  15 + 17 = 32, so:

a = 15

b = 17

h = 27

There are many others ways to split this up.  This is just one.