Grade 10 · Geometry & measurement

Advanced area formulas practice

Advanced area formulas is a grade 10 math skill aligned to Common Core standard HSG.C.B.5: derive the fact that the length of the arc intercepted by an angle is proportional to the radius, and derive the formula for the area of a sector. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 advanced area formulas problems our math games drill.

CCSS HSG.C.B.515 questions in the bank

Sample questions

Try 8 for free

Question 1easy

A triangle has sides $3$ , $4$ , and $5$ . What is its area?

This is a right triangle ( $3$ - $4$ - $5$ ). Area $= \dfrac{1}{2} \times 3 \times 4 = 6$ .

Question 2easy

A rhombus has diagonals of length $6$ and $8$ . What is its area?

Area of a rhombus $= \dfrac{1}{2} \times d_{1} \times d_{2} = \dfrac{1}{2} \times 6 \times 8 = 24$ .

Question 3easy

A right triangle has legs $6$ and $8$ . What is its area?

Area $= \dfrac{1}{2} \times 6 \times 8 = 24$ .

Question 4easy

Find the area of a sector with radius $4$ and central angle $60°$ . Use $\pi = 3$ .

Sector area $= \dfrac{60}{360} \times \pi r^2 = \dfrac{60}{360} \times 3 \times 16 = 8$ .

Question 5easy

A triangle has sides $5$ , $12$ , and $13$ . What is its area?

This is a right triangle ( $5$ - $12$ - $13$ ). Area $= \dfrac{1}{2} \times 5 \times 12 = 30$ .

Question 6easy

A rhombus has diagonals of length $10$ and $12$ . What is its area?

Area $= \dfrac{1}{2} \times 10 \times 12 = 60$ .

Question 7easy

A right triangle has legs $8$ and $15$ . What is its area?

Area $= \dfrac{1}{2} \times 8 \times 15 = 60$ .

Question 8easy

Find the area of a sector with radius $6$ and central angle $120°$ . Use $\pi = 3$ .

Sector area $= \dfrac{120}{360} \times \pi r^2 = \dfrac{120}{360} \times 3 \times 36 = 36$ .

Tests that cover advanced area formulas:

NAEP SAT ACT MCAP NC EOG/EOC

More Grade 10 skills:

Normal distribution basics Unit circle trig values (SAT)Circle equation translations Circle theorems Equation of a circle Midpoint formula Perimeter and arc length Similar right triangle trigonometry All Grade 10 practice →

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