Find areas of triangles, quadrilaterals, and circles.
Free, timed SHSAT practice sets on area of 2d shapes— every question includes a full worked explanation, and there's no account required.
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Area measures the space inside a shape, in square units. Pick the right formula, then plug in carefully.
Common traps: forgetting the \(\dfrac{1}{2}\) for triangles and trapezoids (your answer comes out exactly double), squaring the diameter instead of the radius (4 times too big: \(144\pi\) instead of \(36\pi\)), forgetting to square the radius, and adding sides, which finds the perimeter instead of the area.
Area \(= \dfrac{1}{2} b h = \dfrac{1}{2}(36)(22) = 396\) sq in. (Leaving out the \(\dfrac{1}{2}\) gives \(36 \times 22 = 792\). Halving both the base and the height before multiplying gives 198. Adding the base and the height gives 58.)
Radius \(= 26 \div 2 = 13\), so area \(= \pi r^2 = \pi(13)^2 = 169\pi\) sq in. (Squaring the diameter instead of the radius gives \(676\pi\). Using the circumference formula \(\pi d\) gives \(26\pi\). Squaring the diameter first and then dividing by 2 gives \(338\pi\).)
Area \(= \dfrac{1}{2}(b_1 + b_2)h = \dfrac{1}{2}(14 + 10)(7) = 84\) sq yd. (Leaving out the \(\dfrac{1}{2}\) gives 168. Treating it as a rectangle with the longer base, \(14 \times 7\), gives 98. Averaging the bases and forgetting to multiply by the height gives 12.)