Calculating the length of the side of a quadrilateral - GMAT Quantitative

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The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

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Let be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length . Substitute in the formula for the area of a trapezoid, and solve for :

$$\frac{1}{2}$ (B + b)h = A$

$$\frac{1}{2}$ (B + B - 10) \cdot 24= 1,600$

$24B \div 24 = 1,720 \div 24$

$B = 71 $\frac{2}{3}$$ centimeters

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

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Let be the length of the shorter base. Then is the length of its longer base, and is the height. Substitute in the area formula:

$$\frac{1}{2}$ ( B + b) h = A$

$$\frac{1}{2}$ ( 3b + b) \cdot 6b= 6,000$

$$\frac{1}{2}$ \cdot 4b \cdot 6b= 6,000$

$b = $\sqrt{500}$ = $\sqrt{100}$\cdot $\sqrt{5 }$ =10 $\sqrt{5 }$$

The height is six times this, or $h = 6 \cdot 10 $\sqrt{5 }$ = 60 $\sqrt{5 }$$ inches.

A trapezoid has bases of length one mile and 4,000 feet and height one-half mile. What is the length of its midsegment?

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The length of the midsegment of a trapezoid is the mean of the lengths of its bases; the height is irrelevant. The bases are of length 4,000 feet and 5,280 feet; their mean is

$$\frac{1}{2}$ \left ( 5,280 + 4,000 \right ) = 4,640$ feet, the length of the midsegment.

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

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The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(2500)}{50}$-70=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(1000)}{20}$-60=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(4000)}{40}$-120=b$

$$\frac{8000}{40}$-120=b$

The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

Tap to see back →

Let be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length . Substitute in the formula for the area of a trapezoid, and solve for :

$$\frac{1}{2}$ (B + b)h = A$

$$\frac{1}{2}$ (B + B - 10) \cdot 24= 1,600$

$24B \div 24 = 1,720 \div 24$

$B = 71 $\frac{2}{3}$$ centimeters

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

Tap to see back →

Let be the length of the shorter base. Then is the length of its longer base, and is the height. Substitute in the area formula:

$$\frac{1}{2}$ ( B + b) h = A$

$$\frac{1}{2}$ ( 3b + b) \cdot 6b= 6,000$

$$\frac{1}{2}$ \cdot 4b \cdot 6b= 6,000$

$b = $\sqrt{500}$ = $\sqrt{100}$\cdot $\sqrt{5 }$ =10 $\sqrt{5 }$$

The height is six times this, or $h = 6 \cdot 10 $\sqrt{5 }$ = 60 $\sqrt{5 }$$ inches.

A trapezoid has bases of length one mile and 4,000 feet and height one-half mile. What is the length of its midsegment?

Tap to see back →

The length of the midsegment of a trapezoid is the mean of the lengths of its bases; the height is irrelevant. The bases are of length 4,000 feet and 5,280 feet; their mean is

$$\frac{1}{2}$ \left ( 5,280 + 4,000 \right ) = 4,640$ feet, the length of the midsegment.

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(2500)}{50}$-70=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(1000)}{20}$-60=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(4000)}{40}$-120=b$

$$\frac{8000}{40}$-120=b$

The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

Tap to see back →

Let be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length . Substitute in the formula for the area of a trapezoid, and solve for :

$$\frac{1}{2}$ (B + b)h = A$

$$\frac{1}{2}$ (B + B - 10) \cdot 24= 1,600$

$24B \div 24 = 1,720 \div 24$

$B = 71 $\frac{2}{3}$$ centimeters

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

Tap to see back →

Let be the length of the shorter base. Then is the length of its longer base, and is the height. Substitute in the area formula:

$$\frac{1}{2}$ ( B + b) h = A$

$$\frac{1}{2}$ ( 3b + b) \cdot 6b= 6,000$

$$\frac{1}{2}$ \cdot 4b \cdot 6b= 6,000$

$b = $\sqrt{500}$ = $\sqrt{100}$\cdot $\sqrt{5 }$ =10 $\sqrt{5 }$$

The height is six times this, or $h = 6 \cdot 10 $\sqrt{5 }$ = 60 $\sqrt{5 }$$ inches.

A trapezoid has bases of length one mile and 4,000 feet and height one-half mile. What is the length of its midsegment?

Tap to see back →

The length of the midsegment of a trapezoid is the mean of the lengths of its bases; the height is irrelevant. The bases are of length 4,000 feet and 5,280 feet; their mean is

$$\frac{1}{2}$ \left ( 5,280 + 4,000 \right ) = 4,640$ feet, the length of the midsegment.

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(2500)}{50}$-70=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(1000)}{20}$-60=b$

A given trapezoid has an area of , a longer base of length , and a height of . What is the length of the shorter base?

Tap to see back →

The area of a trapezoid with a larger base , a shorter base , and a height is defined by the equation $A=\frac{1}{2}$(B+b)h$ . Restructuring to solve for the shorter base :

$A=\frac{1}{2}$(B+b)h$

$$\frac{2A}{h}$=B+b$

$$\frac{2A}{h}$-B=b$

Plugging in our values for , , and :

$$\frac{2(4000)}{40}$-120=b$

$$\frac{8000}{40}$-120=b$

The area of a trapezoid is 1,600 square centimeters. Its height is 24 centimeters, and one base is one decimeter longer than the other. What is the length of the longer base?

Tap to see back →

Let be the longer base. Then, since this is ten centimeters (= 1 decimeter) longer than the shorter, the shorter base has length . Substitute in the formula for the area of a trapezoid, and solve for :

$$\frac{1}{2}$ (B + b)h = A$

$$\frac{1}{2}$ (B + B - 10) \cdot 24= 1,600$

$24B \div 24 = 1,720 \div 24$

$B = 71 $\frac{2}{3}$$ centimeters

The area of a trapezoid is 6,000 square inches. Its height is twice the length of its ionger base, which is three times the length of its shorter base. What is the height of the trapezoid?

Tap to see back →

Let be the length of the shorter base. Then is the length of its longer base, and is the height. Substitute in the area formula:

$$\frac{1}{2}$ ( B + b) h = A$

$$\frac{1}{2}$ ( 3b + b) \cdot 6b= 6,000$

$$\frac{1}{2}$ \cdot 4b \cdot 6b= 6,000$

$b = $\sqrt{500}$ = $\sqrt{100}$\cdot $\sqrt{5 }$ =10 $\sqrt{5 }$$

The height is six times this, or $h = 6 \cdot 10 $\sqrt{5 }$ = 60 $\sqrt{5 }$$ inches.