6:[["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"Quiz\",\"name\":\"Geometry and Trigonometry - Area and volume — Quiz 2\",\"description\":\"Area and volume fundamentals.\",\"url\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-2\",\"educationalLevel\":\"Intermediate\",\"numberOfQuestions\":10,\"isAccessibleForFree\":true,\"about\":{\"@type\":\"Thing\",\"name\":\"Geometry and Trigonometry - Area and volume\"}}"}}],["$","script",null,{"type":"application/ld+json","dangerouslySetInnerHTML":{"__html":"{\"@context\":\"https://schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https://theschoolofmathematics.com\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Quizzes\",\"item\":\"https://theschoolofmathematics.com/quiz\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Geometry and Trigonometry - Area and volume — Quiz 2\",\"item\":\"https://theschoolofmathematics.com/quiz/psat-8-9-geometry-area-volume-quiz-2\"}]}"}}],["$","div",null,{"className":"bg-gradient-to-b from-white via-gray-50 to-white","children":["$","div",null,{"className":"container mx-auto px-4 py-8 md:py-12","children":[["$","div",null,{"className":"mb-12","children":["$undefined",["$","div",null,{"className":"mb-8","children":["$","h1",null,{"className":"text-4xl md:text-5xl lg:text-6xl font-bold text-gray-900 mb-4","children":"Geometry and Trigonometry - Area and volume — Quiz 2"}]}],["$","div",null,{"className":"bg-white rounded-2xl shadow-lg p-6 md:p-8 border border-gray-200","children":[["$","div",null,{"className":"text-lg md:text-xl text-gray-700 mb-6 leading-relaxed prose prose-lg max-w-none","dangerouslySetInnerHTML":{"__html":"

Area and volume fundamentals.

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Practice problems focused on area and volume concepts for PSAT 8/9.

"},"excerpt":{"rendered":"

Area and volume fundamentals.

"},"explanation":null,"metaTitle":null,"metaDescription":null,"featured_media":0,"featured_media_url":"$undefined","acf":{"duree_estimee":"$undefined","niveau_difficulte":"Intermediate","categorie":"Geometry and Trigonometry - Area and volume","nombre_questions":10,"score_minimum":80,"ordre_questions":"Fixe","questions":[{"id":"cmrk8f0mr0yatjg8wl5dj9nh2","texte_question":"$19","type_question":"QCM","explication":"

Since the triangles are similar, corresponding side lengths and perimeters have the same scale factor.

Find the scale factor from triangle $$JKL$$ to triangle $$RST$$.

$$\\frac{RS}{JK}=\\frac{135}{15}$$

Simplify.

$$\\frac{135}{15}=9$$

Multiply the perimeter of triangle $$JKL$$ by the scale factor.

$$36 \\times 9=324$$

The perimeter of triangle $$RST$$ is $$324$$.

Final answer: $$324$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$324$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"$$$540$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2916$$

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$$8100$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0mu0yazjg8wrfqgvtj3","texte_question":"

Each side of a square has a length of $$32$$. What is the perimeter of this square?

","type_question":"TexteLibre","explication":"

Use the formula for the perimeter of a square.

$$P=4s$$

Substitute $$32$$ for the side length.

$$P=4(32)$$ Multiply.

$$P=128$$

The perimeter of the square is $$128$$.

Final answer: $$128$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

128

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0mx0yb2jg8w4s9imj7i","texte_question":"

The perimeter of triangle $$XYZ$$ is $$21$$ inches. The length of side $$XY$$ is $$6$$ inches, and the length of side $$XZ$$ is $$8$$ inches. What is the length, in inches, of side $$YZ$$?

","type_question":"QCM","explication":"

Use the formula for perimeter.

$$Perimeter=XY+XZ+YZ$$

Substitute the known values.

$$21=6+8+YZ$$

Add the known side lengths.

$$21=14+YZ$$

Subtract $$14$$ from both sides.

$$YZ=7$$

The length of side $$YZ$$ is $$7$$ inches.

Final answer: $$7$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$5$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$7$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$8$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$13$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0mz0yb8jg8wwftcfgqk","texte_question":"

A rectangle has a length of $$4$$ units and a width of $$27$$ units. Which expression gives the area, in square units, of this rectangle?

","type_question":"QCM","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$4$$ for the length and $$27$$ for the width.

$$Area=4 \\times 27$$

So, the expression that gives the area is $$4 \\cdot 27$$.

Final answer: $$(4) \\cdot (27)$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$2(4+27)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$2(4 \\cdot 27)$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$4+27$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$(4) \\cdot (27)$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0n20ybejg8wtfwmkc1v","texte_question":"

The width of a rectangle is $$9$$ centimeters. The length of the rectangle is $$15$$ centimeters longer than the width. What is the area, in square centimeters, of this rectangle?

","type_question":"QCM","explication":"

The width is $$9$$ centimeters.

The length is $$15$$ centimeters longer than the width.

$$length=9+15$$

$$length=24$$

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$24$$ for the length and $$9$$ for the width.

$$Area=24 \\times 9$$

$$Area=216$$

The area of the rectangle is $$216$$ square centimeters.

Final answer: $$216$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$24$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$135$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$216$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$324$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0n40ybkjg8wehubmlu7","texte_question":"

The area of a rectangle is $$480$$ square inches. The length of the rectangle is $$20$$ inches. What is the width, in inches, of this rectangle?

","type_question":"QCM","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute the known values.

$$480=20w$$

Divide both sides by $$20$$.

$$w=24$$

The width of the rectangle is $$24$$ inches.

Final answer: $$24$$

","points":1,"temps_limite":60,"reponses":[{"texte":"$$$12$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$24$$","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$40$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$460$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0n60ybqjg8w1f5j68pt","texte_question":"

The area of a rectangle is $$84$$ square inches. The length of the longest side of the rectangle is $$12$$ inches. What is the length, in inches, of the shortest side of this rectangle?

","type_question":"TexteLibre","explication":"

Use the formula for the area of a rectangle.

$$Area=length \\times width$$

Substitute $$84$$ for the area and $$12$$ for the longest side.

$$84=12w$$

Divide both sides by $$12$$.

$$w=7$$

The shortest side of the rectangle is $$7$$ inches.

Final answer: $$7$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0n80ybtjg8wkz1rh6ws","texte_question":"

A triangle has a base length of $$30$$ centimeters and a height of $$16$$ centimeters. What is the area, in square centimeters, of the triangle?

","type_question":"TexteLibre","explication":"

Use the formula for the area of a triangle.

$$Area=\\frac{1}{2}bh$$

Substitute $$30$$ for the base and $$16$$ for the height.

$$Area=\\frac{1}{2}(30)(16)$$

Multiply.

$$Area=\\frac{1}{2}(480)$$

Simplify.

$$Area=240$$

The area of the triangle is $$240$$ square centimeters.

Final answer: $$240$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

240

","correcte":true,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0nb0ybwjg8w725ejwn9","texte_question":"

Each base of a right rectangular prism has a length of $$10$$ inches and a width of $$6$$ inches. The prism has a volume of $$1200$$ cubic inches. What is the height, in inches, of the prism?

","type_question":"QCM","explication":"

Use the formula for the volume of a rectangular prism.

$$V=lwh$$

Substitute the known values.

$$1200=10 \\times 6 \\times h$$

Multiply $$10$$ and $$6$$.

$$1200=60h$$

Divide both sides by $$60$$.

$$h=20$$

The height of the prism is $$20$$ inches.

Final answer: $$20$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$10$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$20$$

","correcte":true,"explication":"","imageUrl":"$undefined"},{"texte":"

$$12$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$2$$

","correcte":false,"explication":"","imageUrl":"$undefined"}]},{"id":"cmrk8f0ne0yc2jg8wtblpqlfa","texte_question":"

Triangle $$PQR$$ and triangle $$STU$$ are similar triangles, where $$PQ$$ and $$ST$$ are corresponding sides. If $$ST=3PQ$$ and the perimeter of triangle $$PQR$$ is $$18$$, what is the perimeter of triangle $$STU$$?

","type_question":"QCM","explication":"

Since the triangles are similar, corresponding side lengths and perimeters have the same scale factor.

The side $$ST$$ is $$3$$ times the side $$PQ$$.

$$ST=3PQ$$

So, the scale factor from triangle $$PQR$$ to triangle $$STU$$ is $$3$$.

Multiply the perimeter of triangle $$PQR$$ by $$3$$.

$$18 \\times 3=54$$

The perimeter of triangle $$STU$$ is $$54$$.

Final answer: $$54$$

","points":1,"temps_limite":60,"reponses":[{"texte":"

$$6$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"$$$18$$","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$36$$

","correcte":false,"explication":"","imageUrl":"$undefined"},{"texte":"

$$54$$

","correcte":true,"explication":"","imageUrl":"$undefined"}]}]},"categories":["geometry-and-trigonometry-area-and-volume"],"date":"2026-06-04T09:04:49.341Z","modified":"2026-07-14T05:49:54.286Z"}}],false,["$","div",null,{"className":"mt-10 mb-12","aria-label":"Advertisement","children":["$","div",null,{"className":"my-8 ","children":["$","$L1a",null,{"adSlot":"1234567890","adFormat":"auto","fullWidthResponsive":true,"style":{"minHeight":"250px"}}]}]}]]}]}]]

Geometry and Trigonometry - Area and volume — Quiz 2

Questions in this quiz (10)