Question

1. consider the net of a triangular pyramid composed of four equilateral triangles. what is the surface area of the triangular pyramid? a 56 square inches b 84 square inches c 112 square inches d 224 square inches 2. \\(12\overline{)1296}\\) 3. \\(34.2 \times 6=\\)

Explanation:

Question 1

Step1: Find area of one triangle

The formula for the area of a triangle is $A = \frac{1}{2} \times base \times height$. Here, base = 8 in and height = 7 in. So, area of one triangle is $\frac{1}{2} \times 8 \times 7 = 28$ square inches.

Step2: Find total surface area

The triangular pyramid's net has 4 equilateral triangles. So total surface area is $4 \times 28 = 112$ square inches.

Step1: Divide 1296 by 12

We perform long division: 12 goes into 12 (first two digits) 1 time. $12 \times 1 = 12$, subtract from 12, get 0. Bring down 9, 12 goes into 9 zero times. Bring down 6, now we have 96. 12 goes into 96 8 times. $12 \times 8 = 96$, subtract, get 0. So the result is 108.

Step2: Verify

$12 \times 108 = 1296$, which matches the dividend.

Step1: Multiply 34.2 by 6

We can write 34.2 as 34 + 0.2. Then, $(34 + 0.2) \times 6 = 34 \times 6 + 0.2 \times 6$. $34 \times 6 = 204$, $0.2 \times 6 = 1.2$. Add them together: $204 + 1.2 = 205.2$.

Answer:

C. 112 square inches

Question 2