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Digital SAT · Solve it in Desmos

How to Solve Area and Perimeter on Desmos (Digital SAT)

Where Desmos earns its keep is the backward problem and any messy arithmetic; the equation solves in one line. What it cannot do is pick the formula or spot the perpendicular height, so those stay with you.

Perfect1600 Content Team·Uses the same Desmos calculator that is built into the Digital SAT

Full method for area and perimeter

The Desmos steps

  1. 1

    Enter the formula with numbers

    Type it straight in, such as 0.5 * 10 * 7 for a triangle, and read the result.

  2. 2

    Turn it into an equation for a missing side

    Type the formula set equal to the known area or perimeter and let Desmos return the solution.

  3. 3

    Confirm the units

    Square units for an area, plain units for a perimeter, before you commit to a choice.

Worked in Desmos

Easy example
A rectangle has a length of 15 meters and a width of 8 meters. What is the perimeter, in meters, of the rectangle?
A
23
46
C
61
D
120

A: This adds the sides once but forgets to double, 15 + 8 = 23.

B: Perimeter = 2(length + width) = 2(15 + 8) = 46.

C: This adds one extra side to the perimeter, 46 + 15 = 61.

D: This is the area, 15 × 8 = 120, not the perimeter.

Explanation

Perimeter = 2(length + width) = 2(15 + 8) = 46 meters.

Detailed explanation

Add the length and width, then double: 2(15 + 8) = 46.

Easy example
A triangle has a base of 10 and a height of 7. What is the area of the triangle?
A
17
B
34
35
D
70

A: This adds the base and height instead of using the area formula.

B: This doubles the sum of base and height, which is not the area.

C: Area of a triangle = ½ × base × height = ½ × 10 × 7 = 35.

D: This uses base × height but forgets the factor of ½.

Explanation

Area =12(10)(7)=35= \frac{1}{2}(10)(7) = 35.

Detailed explanation

The area of a triangle is 12bh=12(10)(7)=35\frac{1}{2}bh = \frac{1}{2}(10)(7) = 35.

Easy example
A square has a side length of 12. What is the area of the square?
A
24
B
48
144
D
288

A: This adds the two side lengths, 12 + 12 = 24, instead of multiplying.

B: This is the perimeter, 2(12 + 12) = 48, not the area.

C: Area = length × width = 12 × 12 = 144.

D: This doubles the area.

Explanation

Area =122=144= 12^{2} = 144.

Detailed explanation

The area of a square is the side squared: 122=14412^{2} = 144.

Try it with the calculator

Question 1easy

A rectangle has a length of 7 and a width of 9. What is the area of the rectangle?

Question 2easy

A square has a side length of 11. What is the perimeter of the square?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Desmos questions

Can Desmos solve area and perimeter questions on the SAT?

Where Desmos earns its keep is the backward problem and any messy arithmetic; the equation solves in one line. What it cannot do is pick the formula or spot the perpendicular height, so those stay with you.

Is the Desmos calculator really built into the Digital SAT?

Yes. The Bluebook testing app includes the Desmos graphing calculator on every Math question, so the method here is one you can use on test day, not a workaround.

Should I still learn the algebra?

Yes. Desmos is fastest when you know what to type and what to read. Learn the underlying method on the full guide, then use the calculator to move quickly and to check your work.

Master area and perimeter, calculator and all

Every Digital SAT question type comes with the method, the Desmos shortcut, and free practice with instant feedback.

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