Becky is making a spice shelf in the shape of a triangle to fit in the corner of her kitchen cabinet. The triangle's base is 16 inches long, and its area is 96 square inches. Which equation can you use to find the triangle's height, h? Choices: (A)96 = 1/2(16)h (B)96 = 2(16)h What is the triangle's height? Write your answer as a whole number or decimal. Do not round. ____ inches

Identify formula: Step 1: Identify the correct formula to calculate the height of the triangle. We know the area of a triangle is given by the formula: Area = 1/2(base × height). For Becky's triangle, the base is 16 inches and the area is 96 square inches. We need to find the height, h. The correct equation to use is: Area = 1/2(base × height) 96 = 1/2(16 × h) This corresponds to choice (A): 96 = 1/2(16)h Calculate height: Step 2: Solve the equation for h. Starting with the equation from Step 1: 96 = 1/2(16 × h) Multiply both sides by 2 to eliminate the fraction: 2 × 96 = 16 × h 192 = 16h Now, divide both sides by 16 to solve for h: h = 192 / 16 h = 12

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Becky is making a spice shelf in the shape of a triangle to fit in the corner of her kitchen cabinet. The triangle's base is $16$ inches long, and its area is $96$ square inches. $\newline$ Which equation can you use to find the triangle's height, $h$ ? $\newline$ Choices: $\newline$ (A) $96 = \frac{1}{2}(16)h$ $\newline$ (B) $96 = 2(16)h$ $\newline$ What is the triangle's height? $\newline$ Write your answer as a whole number or decimal. Do not round. $\newline$ ____ inches $\newline$

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Grade 6

Area of quadrilaterals and triangles: word problems

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Q. Becky is making a spice shelf in the shape of a triangle to fit in the corner of her kitchen cabinet. The triangle's base is

16

inches long, and its area is

96

square inches.

\newline

Which equation can you use to find the triangle's height,

h

\newline

Choices:

\newline

(A)

96 = \frac{1}{2}(16)h

\newline

(B)

96 = 2(16)h

\newline

What is the triangle's height?

\newline

Write your answer as a whole number or decimal. Do not round.

\newline

____ inches

\newline

Identify formula: Step $1$ : Identify the correct formula to calculate the height of the triangle. $\newline$ We know the area of a triangle is given by the formula: Area = $\frac{1}{2}(\text{base} \times \text{height})$ . For Becky's triangle, the base is $16$ inches and the area is $96$ square inches. We need to find the height, $h$ . The correct equation to use is: $\newline$ Area = $\frac{1}{2}(\text{base} \times \text{height})$ $\newline$ $96 = \frac{1}{2}(16 \times h)$ $\newline$ This corresponds to choice (A): $96 = \frac{1}{2}(16)h$
Calculate height: Step $2$ : Solve the equation for $h$ . Starting with the equation from Step $1$ : $96 = \frac{1}{2}(16 \times h)$ Multiply both sides by $2$ to eliminate the fraction: $2 \times 96 = 16 \times h$ $192 = 16h$ Now, divide both sides by $16$ to solve for $h$ : $h = \frac{192}{16}$ $h = 12$