3 Replies Latest reply on Jul 11, 2018 12:29 PM by Chrys C.

# Praxis Core for Dummies, with online practice tests

I am studying for the Praxis math and have run into an issue one of the practice tests in the book (not online). Page 256-257, question #13 states the following: The preceding pyramid has a square base, a height of 9 cm, and a volume of 342 cm3. What is the surface area of the pyramid rounded to the nearest whole number.

If you go to page 298-299, which contains the answer to question #13, and the book has that answer at 260 cm3.

The trouble I am running into is the formula used to find the Surface Area is .5 times (P)erimeter times slant (l) height (.5Pl), written into the explanation of the answer.

Looking on page 96, the formula for finding Surface Area is B + .5Pl. Which one is it?

.5 times Pl is lateral area, which plugged into the question gets an answer of 259.2 cm3, rounded up to 260 which is the answer given.

However, using the formula B + .5Pl (surface area of a pyramid) you get an answer of 404 cm3.

• ###### Re: Praxis Core for Dummies, with online practice tests

Hello Tim,

Thank you for your post!

I will need to inquire with the editor for a solution. Would you mind responding with the ISBN of your book?

Have a nice evening!

- Chrys

• ###### Re: Praxis Core for Dummies, with online practice tests

Sir, thank you for you response.

ISBN # 978-1-118-53280-5

Timothy J. Smith

314-800-8129

Miraphone 1201

PT 66/65

• ###### Re: Praxis Core for Dummies, with online practice tests

Hello Tim,

Thank you for this information!

Unfortunately, this first edition title is out of print so I won't be able to reach the editor for a solution. I'm sorry for any inconvenience!

If it helps, the new question 13 in the second edition (ISBN: 978-1-119-38240-9) is:

Question:

13. The preceding pyramid has a square base, a

height of 9 cm, and a volume of 432 cm^3. What

is the lateral area of the pyramid rounded to

the nearest whole number? (Lateral Area = ½Ps

where P is the base perimeter and s is the slant

height).

(A) 108 cm^2

(B) 135 cm^2

(C) 260 cm^2

(D) 520 cm^2

(E) 2,808 cm^2

13. C. 260 cm2

This problem requires you to take what you know and use it to work your way to what you

don’t know.

The formula for the volume of a pyramid is 1/3Bh. The volume and height of the pyramid are

given, so you can put those values into the formula and solve for B, base area. This process

reveals that the base area is 144 cm^2.

The base is a square, so the sides have equal measures. The measure of a side times itself

gives the area of the square, so a side is equal to the square root of the area. The square root

of 144 is 12, so each side is 12 cm.

That means the distance from the center of the square base to the midpoint of one of its

sides is 6 cm. The center-midpoint segment, the segment representing the height of the

pyramid, and a segment representing the slant height of the pyramid form a right triangle.

By using the Pythagorean theorem, a^2 + b^2 = c^2, you can determine that the slant height of

the pyramid is approximately 10.8 cm.

With the information gathered so far, you have what you need to use the formula for the lateral

area of a pyramid, which is 1/2 times perimeter times slant height. By putting the known

values into the formula, you can conclude that the lateral area of the pyramid, to the nearest

whole number, is 260 cm^2.

Does this help?

Have a nice afternoon!

- Chrys