Solved Problem 1: Side of a Triangle

Grade Level: 3 – 6

Starting now, we will be solving some problems with detailed solutions. Today, we’ll start with a problem about square and triangle.

Problem

The side of square ABCD is 12 cm. Point P is drawn on side AB and then connected to D. If the area of triangle APD = 60 square centimeters, what is the length of AP?

mtap reviewer square and triangle

Solution

The area of a triangle is the product of half of its base and height. ABCD is a square, so A is a right angle; therefore, we can take AP and AD as base and height. We let AP = nContinue reading

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Grade 1 MTAP Reviewer Set 8

1.)  There are 18 apples and 4 children. If 3 apples are given to each pupil, how many apples are left?

2.) A box has how many corners?

a. 4
b. 6
c. 8
d. 12

3.) Fill in the blank with the correct number.

45 – 12 = 8 + ___

4.) What is the sum of 12 tens and 7 ones?

5.) Faye started studying at 7:30 pm. If she studied for 45 minutes, what time did she finish?

6.) Arrange the following numbers from smallest to largest:

11 – 6, 2 + 5, 3 + 6, 8 – 4, 16 – 10  Continue reading

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Grade 6 MTAP Reviewer Set 8

1.) Which of the following numbers does not belong to the list:

12, 17, 22, 27, 32

2.) What should be subtracted from 3 to get 13/5?

3.) The sum of the digits of a 2-digit number is 13. When the digits are reversed, the new number is 27 less than the original number. What is the original number?

4.) The exterior of an open box is to be covered with gift wrapper. If the dimensions of the box are 5 by 8 by 12, and 5 is its height, what is the least gift wrap needed?

5.) The side lengths of the triangle are 4 cm, 4cm, and 5cm. Which angles are equal in measure?

acute triangle

6.) Find the next number in the list below.  Continue reading

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Problem of the Week 8

This is the 8th problem of the week of MTAP Reviewer.

Problem

The diagonal of a square is 6cm. Find the area of the square that is twice its size.

Solution

We can divide a square into several ways, one of which is using its diagonal.

square
Click on the image to enlarge

Now, using the diagonal of the square as side of the larger square, we can create a larger square as shown above. As seen, the diagonal of the square cuts the square into half. This half region makes a fourth of the larger square (Can you see why?).

Since the length of the side of the larger square is the diagonal of the smaller square 6, the area of the larger square is 6× 6 = 36.

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