Question

Triangle D E F is shown. The length of E F is 10, the length of D F is 7, and the length of D E is 12. What information relevant to calculating area do we have available for this triangle? Which method should we use to calculate the area for this triangle? What is the area of this triangle calculated to the nearest hundredth of a square unit?

Answer 1

SSS, Heron's formula, and 34.98 square units

Explanation:

Answer 2

34.98 square units.

Explanation:

It is given that DEF is a triangle, EF=10, DF=7 and DE=12.

Information of sides of triangle is relevant to calculating area.

We should use Heron's formula.

According to Heron's formula, the area of triangle is

`A=√(s(s-a)(s-b)(s-c))`

where,

`s=(a+b+c)/(2)`

For triangle DEF, let a=10, b=7 and c=12.

Now,

`s=(10+7+12)/(2)=(29)/(2)=14.5`

Area of triangle is

`A=√(14.5(14.5-10)(14.5-7)(14.5-12))`

`A=√(14.5(4.5)(7.5)(2.5))`

`A=√(1223.4375)`

`A=34.977671`

`A\approx 34.98`

Therefore, the area of triangle DEF is 34.98 square units.